Maybe Arsène Wenger does know after all. An unbalanced, transitional, sometimes lightweight Arsenal team produced one of the most see-sawingly unlikely third‑place finishes in recent Premier League history with a victory at The Hawthorns that, but for Kieron Gibbs's late tackle, might have been a calamitous 3-3 draw. In the process they ensured the fiscal grail of Champions League qualification continued: shaken, stirred but as yet uninterrupted. At the end Wenger appeared both calm and commendably magnanimous after a season that had also brought occasional animosity from a vocal minority of the club's support.

"I'm very proud of this season," Wenger said. "We were tested not just on the pitch but off, for our unity and solidity in the club. We didn't show weakness and we stayed united. It's a good lesson for everyone.

"If you look at the season as a whole we only lost two in the last 16 games, we had a fantastic run and finished with a respectable 70 points and qualified for the 15th year in a row for the Champions League and we are proud of that. Only three clubs in the whole of Europe have done that. It shows it's not as easy as it looks."

Wenger conceded it had been a close run thing during a match that seemed to pulse along at its own frenzied tempo. "I felt when we were 1-0 up we looked nervous and shaky. At 2-1 down we got back to our game and we defended crosses with resilience. I'm still thinking of suing the referee for the five minutes of added time, because my heart suffered too much."

Gibbs received particular praise after a late appearance at left-back from the bench that steadied an initially harum-scarum back four. "He came on very well," Wenger said. "We suffered on that flank in the first half. He won headers and tackles and he deserves huge credit for that tackle."

Of Robin van Persie's decision after the other players had left the pitch to walk across, defying the attentions of stewards, and enjoy a protracted communion with the travelling support, Wenger remained wryly noncommittal. "You can make of that what you want. If he didn't celebrate, you would say he's already gone. If he does, you can say he's saying goodbye. I would see it as a positive." Talks are planned before Van Persie leaves to join the Dutch camp for Euro 2012. His fate is perhaps undecided right now but it was a moment no doubt designed to save the Dutchman from feeling he never got the chance to say goodbye.

As for Roy Hodgson, in some ways this was an ideal final Premier League workout for England's new manager. Charged with deploying his team of energetic middleweights to stifle apparently superior cosmopolitan opponents, Hodgson drew another well-drilled and even expansive performance from his players, sending his final West Bromwich Albion team out in an adventurous 4‑4‑1‑1 formation.

Hodgson also maintained his commendably low-key persona so far by dodging the post-match press conference, sending instead his No2 Keith Downing, who paid generous tribute to his departing boss. "Roy has given the club a stability, a structure, improving the standard every day. He's making players, even when they're 30 years of age better in their game," Downing said.

"There are a lot of players in the dressing room disappointed to see him go. People talk about senior players [with England] but senior players can learn. Roy will give honesty and integrity, a shape and a system that players will understand. He's got all the attributes to do a decent job at national level."