The Gunners finally made sure of qualification for the group stages of the Champions League for a 15th season when they beat West Brom 3-2 in a tense final day at The Hawthorns to edge ahead of rivals Tottenham by just a point.
It is a remarkable achievement in itself considering how far off the pace Arsenal were earlier in the campaign, having slumped as low as 17th after losing four from the opening seven league games.
Despite the disappointments of failing to deliver a trophy once again, Wenger never lost faith in his players.
"I maybe take the biggest ever [satisfaction] because at some stage of the season everybody would have said you were absolutely mad," Wenger told Arsenal Player.
"We still kept our focus and worked hard together.
"It is down to remarkable character and I am very proud of the achievement of the team."
Arsenal's resurgence following a run of nine wins out of 10 games from February 4 means they now do not have to sweat on the outcome of the Champions League final - which Chelsea will have to win to take the place of Spurs in next season's elite club competition.
"It is good to sleep better at night," Wenger said.
"It is a tricky position in fourth because you don't want Chelsea to win the Champions League, and to be fourth is playing a qualifier, which every year is more difficult.
"Therefore just to be in the group stage straight away is fantastic."
Top of Wenger's to-do list ahead of the European Championships is to sit down with captain Robin van Persie and discuss the future, with the Holland forward so far coy over his intentions.
Without Van Persie's 30 league goals, the Gunners would have been cut adrift, but it remains to be seen whether his extended lone appreciation in front of the travelling Arsenal fans at the end of yesterday's game was a last goodbye, the 28-year-old still with a season left on his current deal.
Whatever happens in 2012/13, winger Theo Walcott maintains Arsenal must believe in their ability to finally end their quest for silverware.
"It was tight, but we have deserved it [third place], for the past few weeks anyway," Walcott said.
"A couple of new additions may come, but we have to push on as it has been so long without a trophy now.
"We just need to start believing a bit more.
"The belief came in September that we really wanted it.
"If we can do that right from the start, keep people fit, then you never know where it will take us next year."