On one side there was delighted admiration for a revelation of character under supreme duress, on the other a scathing contempt for a team who were considered to have abdicated all responsibility for playing the game in a way that might entertain the multitudes and inspire impressionable children. You really would not believe we had witnessed the same match.

The distinction, inevitably, was geographical, between England and Spain. Somewhere in between, interestingly enough, came the editors of L'Equipe, France's daily sports paper, whose front page on Wednesday morning was emblazoned with a banner headline "Héroïque Chelsea".

You might have expected L'Equipe, as representatives of the nation that invented the European Cup, to have sided with the purists and lament the failure of Barcelona's artistry to carry the day. Instead it chose to highlight the salient characteristics of Chelsea's performance, with no hint of dismay that obduracy and pragmatism had emerged victorious.

If a side could come away from a match with a statistic indicating that they had enjoyed 84% of the overall possession yet still not win, an argument could be made that they did not deserve a better fate. Maybe Barcelona were collectively tired, maybe important individuals – notably a dispirited Lionel Messi and the usually immaculate Xavi Hernández – had lost form at the end of a long season, but perhaps they also suffered from an understandable assumption that their cherished method would prevail once again, and from the lack of an alternative resource when that turned out not to be the case.

True, they hit the frame of Chelsea's goal four times over the two legs of the tie. But on only one of those occasions – Messi's shot in the 83rd minute of the second match, diverted on to a post by Petr Cech – could they blame anything other than their own profligacy. Alexis Sánchez should have scored at Stamford Bridge, and it was nothing short of unbelievable to see Messi strike a penalty against the crossbar early in Wednesday's second half. Only a couple of weeks ago he was taking two penalties in a single match, and aiming them to different sides of the goalkeeper with such cool precision that you imagined he could never miss. There were plenty of other chances for them in the 180 minutes and Cesc Fábregas was notably wasteful in the first match against Chelsea, allowing Ashley Cole to clear off the line.

So they had their opportunities and were able to take only two of them. Chelsea had one chance in the first match and two in the second, and took all three. The way football works, Chelsea won.

"Anti-football" is the term some people would use to describe the approach adopted by Roberto Di Matteo's side. But when you have been through a season like theirs, and you are facing opponents generally acknowledged to be among the best club teams assembled in the entire history of football, what are you supposed to do? In particular when some of you are still nursing a grievance from what is seen as an unjust elimination by the same opponents at the equivalent stage three years ago.

The concept of "anti-football" is normally brought into play when a team systematically attempt to use illegitimate means to frustrate their opponents. But although the game contained a normal number of fouls and a handful of yellow cards, the offence that led to John Terry's expulsion was an exception to his side's general approach, which was to play with dogged tenacity but stay inside the laws. Chelsea may have played the first half with a 4-5-1 formation and the second with 6-3-0, but they never attempted to kick Barcelona out of the tie. They simply applied themselves to a limited range of options – like a pianist using only the lower half of the keyboard – and worked hard on maintaining their concentration.

"The best team doesn't always win," Torres admitted afterwards, but you would not find a Chelsea player who believed they had been the beneficiaries of an injustice – and to judge by Wednesday's coverage in L'Equipe's and Italy's La Gazzetta dello Sport, not many neutrals, either. The west London club's representatives had dug deep into their store of pride and resilience, and it was enough to see them home. That was something to acknowledge and applaud. They had also saved us from the possibility of enduring a final between two clubs from the same country, an offence against the original spirit of the competition.

And so, at the end of an undistinguished season for the Premier League in Europe, perhaps the least likely club of all stand on the brink of the greatest achievement, with the twist that Chelsea's success in reaching the final neatly upends all the received wisdom about the crucial importance of internal stability. If the story of the first seven months of their season was one of accelerating decline and demoralisation, the past seven and a half weeks – since the dismissal of André Villas-Boas and the promotion of Di Matteo – have shown what a group of players can do when they feel empowered.

Who better than Chelsea, after all, to show that there are more ways to achieve success than the sort of continuity seen in recent years at Manchester United and Arsenal and, going further back, by the giants of the Anfield boot room? It was at Stamford Bridge that José Mourinho demonstrated the virtues of swift, decisive action in the areas of recruitment and tactics – and, funded by an indulgent billionaire, he delivered unprecedented success straight away. Next he pulled off the same trick at Internazionale, where a squad of bedraggled underachievers was transformed through the addition of shrewd buys – Samuel Eto'o, Wesley Sneijder, Thiago Motta and Lúcio – and the application of tactical rigour.

Before Wednesday, Mourinho was also the last coach to eliminate Barcelona from the Champions League, with a more advanced and adventurous version of the game Chelsea played this week. And last Saturday the same coach, now in charge of Real Madrid, all but ended Guardiola's run of Spanish league championships. Although Di Matteo lacks the depth of talent assembled by Mourinho at any of his clubs and has not had the opportunity to make his own additions to the squad, it is hard to believe that he did not make an intelligent appraisal of the way the Portuguese manager approached the task of stifling Barcelona's creativity.

Roman Abramovich was not present at the Camp Nou to watch his team succeeding through the use of methods that had little to do with the sort of spectacle he envisaged after watching a dazzling match between Manchester United and Real Madrid and falling in love with the glamour of big nights in European competition. Given Chelsea's recent history, however, the chance of a trip to Munich next month represents nothing short of a miracle. Whether it is the last flourish of an era or a first sign of rebirth remains to be seen.