Arsène Wenger acknowledged Arsenal’s players have risen to the challenge as they attempt to rescue a top-four finish from a season that appeared to be heading for disaster just a fortnight ago.

Since the defeat against Tottenham Hotspur last month, Arsenal have recorded three consecutive victories over Manchester United, Southampton and Stoke to keep alive their hopes of qualifying for the Champions League. Another win over Sunderland on Tuesday would ensure their challenge goes to the final day of the season and Wenger admitted the performance in Saturday’s first win in Staffordshire since 2010 was testament to his team’s new-found resilience.

“After a difficult period we could have got divided but we have chosen to be united and that’s what you see on the pitch,” he said. “We’ve had to go to places where we have traditionally struggled. That shows that if the confidence is high and the team is focused then anything is possible. We didn’t play as badly as some people have said in the defeats at Palace and West Brom but we were not defensively strong enough. Now we are defensively much better and then the longer games go on, the more confident we are.”

Had the referee, Mike Dean, spotted Peter Crouch’s cheeky handball for his ninth career goal against Arsenal, it would have been a third clean sheet in a row for Wenger’s side. As it was, he had to make do with an emphatic victory over a Stoke side who only showed any interest in attacking for five second-half minutes when the former England striker was introduced from the bench.

Goals from Alexis Sánchez, who limped off immediately afterwards but is expected to be fit for the match on Tuesday, and a second for Olivier Giroud eventually settled Arsenal’s nerves as Stoke conceded four goals in match for the seventh time this season. A pre-planned lap of honour to mark their last home game went ahead despite the vast majority of supporters having long left their seats to head home and Mark Hughes recognised that a few murmurs of discontent are beginning to resurface after a poor end to the season.

“This year has been a disappointment in terms of what we have been able to produce but the last three years we’ve surpassed everybody’s expectations so maybe this is just a plateauing of where we are,” he said. “It gives us an opportunity to kick on and that’s what we intend to do.”

Wenger has yet to confirm he will still be in charge next season despite reports in France over the weekend that he has agreed a one-year deal. But his comments on Chelsea’s title win under Antonio Conte certainly hinted that he is ready to fight another day.

“I take advantage to congratulate Chelsea but we will see when they are playing in Europe it will be a different story,” he said. “We struggled a lot after what happened to us against Bayern Munich. It was a big blow. At that stage it was still possible to come back and challenge Chelsea. The last two years the team who have won the title have not been playing in Europe, so we will see.”