Arsène Wenger's displeasure was easily understandable as he ended the match raging at the referee who had shown Robin van Persie a second yellow card, and the Frenchman continued his diatribe in his post-match interviews. But now he needs to lay aside that sense of injustice and give attention to some of the deep-lying issues exposed by Tuesday night's elimination from the second of the four competitions that were still in Arsenal's sights a mere week and a half ago.

On Saturday night Arsenal travel to Old Trafford, where they meet Manchester United in an FA Cup sixth-round tie which could reduce their list of targets to one or, if the evening goes well, and given that United lie only three points ahead of them in the Premier League table, renew the hopes that another Double, the third of the Wenger era, could be on the cards.

"This is when a manager earns his money," George Graham, a former Arsenal manager, remarked on Talksport, and it is hard to imagine his successor getting much sleep between now and the weekend as he plots to arrest the sudden disintegration of a side that until very recently looked like fulfilling all the potential he has so insistently claimed on their behalf.

Only three weeks ago we were acclaiming perhaps the greatest performance of Wenger's decade and a half in north London, when they took on the world's best club side and prevailed not just through speed and skill but courage and sheer will to win, the very qualities they had so often been accused of lacking. In truth, they were fortunate that Lionel Messi so untypically missed two clear chances to score and that the referee denied Barcelona a plausible penalty claim, but still there were signs that Wenger's constant reiteration of a belief in his side's "spirit" indeed had some substance.

On Tuesday, however, their virtues were blown away and only the flaws remained. They may have been within one decent Nicklas Bendtner finish of smuggling themselves through to the next round, but such an outcome would have been an offence against natural justice, whatever Wenger and Van Persie might say.

The surprise was in the way Arsenal approached the match. Wednesday morning's Spanish papers were withering in their condemnation of the English side's disinclination to attack, a derision compounded by Arsenal's failure to complete their mission. Spanish observers did not like it when José Mourinho ordered Internazionale to pack their defence in last year's semi-final, but at least Mourinho's success earned him a measure of respect.

The scornful cartoon in Mundo Deportivo had Wenger reading from the Mourinho coaching manual: "The fault for not having a shot on goal ... is the referee's, the referee's, the referee's, the referee's, the referee's." But when he reflects on Tuesday's events, he can hardly be proud that his side became the first since 2004 to fail to register a single shot in a Champions League match.

Dismay and perhaps even a measure of shame are the proper responses to such a lamentable feat. Barcelona are a wonderful team, but they were playing with two replacement centre-backs. Despite the freakishness of the possibility that Bendtner could have put his side through to the last eight, Arsenal did nothing to deserve any form of reward. The absence of Thomas Vermaelen, Alex Song and Theo Walcott played a part, and the marginal condition of Van Persie and Cesc Fábregas was clearly unhelpful. But the displays of Tomas Rosicky, Abou Diaby and Bendtner in particular cast doubt on Wenger's readiness to invest further deposits of faith in players who have spent most of their Arsenal careers underperforming.

Diaby, positioned alongside Jack Wilshere in front of the defence but with a relatively free commission, again highlighted the inability or unwillingness of Wenger to plug the gap left by the likes of Patrick Vieira and Gilberto Silva. A strong, driving midfield player used to be an Arsenal characteristic, and Javier Mascherano showed how it should be done, even in a side fundamentally dedicated to attack. Argentina's captain, one imagines, is a player Wenger could have acquired a few years ago, although he might not have fancied doing business with Kia Joorabchian.

Rosicky and Samir Nasri were virtually absent from a game in which they were given enough scope to make an impact. Nasri, so stunningly effective in the first half of the season, seems to have forgotten that his best contributions come when, like Messi, he takes on opponents at close quarters in the penalty area. As for Bendtner, his heavy touch was as apparent as it had been in South Africa last summer, the point at which Wenger should have cut his losses on the Dane.

Eavesdropping on Arsenal supporters during the flight to Catalonia, it was interesting to hear one of them compare Wenger to L Ron Hubbard, the founder of Scientology. "What Arsène's running isn't a football club – it's a cult," the fan said. Barely even half-joking, he was representing that large section of the support to whom Wenger's pursuit of his vision has been too single-minded, and that a more flexible and realistic attitude to investment and recruitment would have long ended the drought since the club's last trophy. What they want is for Arsenal to act like the other big clubs. To them, that means buying an Andy Carroll rather than a Marouane Chamakh, or splashing out on the established qualities of a Mascherano rather than hoping for a Song or a Diaby to mature.

To accept such criticisms, and to take the appropriate action, would require a radical change in Wenger's approach. It would mean admitting that for several seasons his squad has lacked a balance of skill and strength, of artistry and resilience, of fantasy and functionality. Given the strength of his convictions, that seems unlikely to happen – which means that Arsenal's fans, however much they admire his integrity, cannot seriously expect the future to live up to the past any time soon.