Roberto Martínez may well be the Premier League's most polite manager but he was unintentionally damning in his praise of his opponents after this match when he ventured: "Credit to Liverpool, they didn't just come to make up the numbers." It says something when the manager of Wigan feels moved to congratulate Liverpool for their pluck – at Anfield.

What this says is that Liverpool are far from the force they once were and far from the Premier League force that the club's owners thought they would become after Kenny Dalglish was given more than £100m to spend since replacing Roy Hodgson as manager in January 2011.

Liverpool now have three points fewer than they had at this stage last season and are jostling to stay above Everton, Sunderland and Swansea City rather than keeping pace with Arsenal, beleaguered Chelsea or even Newcastle. The doctrine of Dalglish infallibility has been renounced at Anfield, where there is increasing doubt about his judgment.

The chief criticism concerns his transfers. Dalglish complained that a busy fixture list had left his team jaded going into the game against Wigan and he would have liked to have been able to rotate more during the three fixtures the team had in the last week.

But Andy Carroll, for instance, has started only one of the last six league matches and Jordan Henderson has completed only two of the last 10. Grumbling about the squad being overstretched sounds hollow when the manager regularly chooses to park players for whom he paid over £50m on the bench.

Nor is the quibble over fixture congestion convincing. While it is true that Liverpool have fielded strong sides as they advanced in both domestic knockout tournaments – winning the Carling Cup and set to compete in the semi-finals of the FA Cup – their schedule has been eased by not competing in Europe for the first time since 1999.

Dalglish's tactical acumen is also under fire. He has changed his formations and personnel frequently this season and often they have seemed incompatible. Against Wigan the players seldom seemed on the same wavelength and at times the strategy was counterintuitive.

Liverpool began with a 4-1-4-1 apparently designed to provide Luis Suárez with the regular support he often lacks but their best balls in the first half were the sort of sumptuous crosses from Steven Gerrard and Stewart Downing that Carroll might have relished. Yet when Carroll came on at half-time with Liverpool a goal down to Shaun Maloney's penalty, the crosses dried up. Liverpool did equalise through Suárez but soon fell behind again to a Gary Caldwell goal and never looked like recovering.

The inability of Liverpool's midfield to discomfort Wigan when they had the ball lend credence to Dalglish's claim that his players were tired from their heavy recent schedule but raised questions as to why he had chosen to introduce Carroll for Jordan Henderson rather than Dirk Kuyt or Jay Spearing, as the well-rested Henderson was the one midfielder who seemed full of energy and his passing had been no more wasteful than most of his team-mates.

None of that, of course, is of any concern to Wigan who, with this victory, received a mighty boost to their more modest ambition of simply staying in the league.

Like Liverpool, however, Wigan have failed to garner sufficient points at home this season – this was their fourth league win on the road but they have prevailed only once at the DW Stadium – but Martínez is convinced that pattern will change in time to keep the club in the top flight.

"We've had six draws at home this season and I could go through each of them and explain why we didn't win because we were better than the opposition in every department but we just did not have the composure in front of goal and maybe a bit of luck," he said.

"If we had five more wins at home to our name, no one could be surprised but those are the margins. We are in the position we are in because we have not scored enough goals despite scoring enough chances. Clearly we are a very good side but just not a lucky side. Against Liverpool we had the composure and possibly the luck, so we can take big belief from that.

"Overall we deserved three points and that is a major statement when you consider who we are and who Liverpool are. It is a huge boost. We played well in our previous six games – except for Swansea – and we never got the wins; we got four draws and that is eight dropped points. Eight points could put you halfway up the table but where we are now eight points are so difficult to get.

"Every win is extra important and in many ways it can give you belief and confidence and make things easier. But we need to forget about what is happening elsewhere and focus on points we can get. It is about ourselves. But winning at Anfield gives you things you cannot control on the training ground: belief, confidence and a feelgood factor."

Man of the match Gary Caldwell (Wigan Athletic)