The Gunners saw their own championship hopes ended by successive away defeats to Tottenham and then Wigan after dragging themselves back into contention earlier this season.
They went on to secure third place - and with it automatic qualification place in next season's Champions League - after beating a much-changed Fulham side, who had one eye on the Europa League final, 4-0 at the Emirates Stadium.
Wenger, however, insists had Arsenal - who finished some 11 points off the pace - not lost the likes of Robin van Persie, captain Cesc Fabregas and defender William Gallas at various stages of the campaign, then the final-day outcome could have been much different.
"Congratulations to Chelsea, to Carlo Ancelotti and his players. He behaved very well the whole season," said the Arsenal boss.
"For us it was important to finish well and we did it.
"We have gone beyond expectation, if you look at July, but of course we are still frustrated, because one month ago we were in touch with the championship, but did not win it.
"Overall we had a season with a good attitude and strong character, the team has improved a lot on that front, but overall we conceded too many goals to win the championship.
"We did not have the players available in the last six weeks to fight for the championship.
"When you go into the final sprint, you need your squad available.
"We had too many injuries."
Wenger continued: "It is a shame because we have gone out in the quarter-finals of the Champions League to the holders and have been beaten by Chelsea and Manchester United, who have strong squads.
"We were just a fraction short."
Wenger is set to strengthen the squad in the summer, with the arrival of long-term target Marouane Chamakh set to be officially announced before the World Cup.
The Gunners boss, though, insists major additions are not necessary.
"Is a lot of strengthening a number or quality?" Wenger said.
"We want to improve in quality, not necessarily a big number of players needed."
The Arsenal boss continued: "What the fans want concerns me. We both love the club and want the best possible team.
"But we live in a world not to be crazy.
"We have to pay our wages at the end of the month and we have to respect our business rules."
Andrey Arshavin capitalised on a mistake from goalkeeper Mark Schwarzer to give Arsenal the lead after 21 minutes, before Robin van Persie fired in a second, with Chris Baird bundling in an own goal just before the break.
Fulham, who face Atletico Madrid in Hamburg on Wednesday, made eight changes, and substitute Carlos Vela rounded off a comfortable win with four minutes left.
Cottagers boss Roy Hodgson reflected: "I do not think it was difficult to keep the team which I selected focused, because many of them were very much really in need of a game and should have been looking to show what they can do.
"So I take the responsibility that to expect the players to come here and get a result was far too big an ask.
"I am actually quite satisfied with the way they went about things and kept battling against enormous odds.
Hodgson quipped: "Schwarzer is blaming the pitch, saying it took a bobble, but nobody believes him!
"I am pleased to see he has got it out of his system because he has made so few this season, if any."