Wenger's 750th English Premier League match in charge of the Gunners ended in a 1-0 victory over Norwich City at the Emirates Stadium thanks to substitute Danny Welbeck's second-half goal on Sunday (AEST).
But some Arsenal fans in a divided home support held up banners opposing the Frenchman in the 12th and 78th minutes - referencing the 12 years since their last title success.
Wenger concedes that missing out on this season's title is a major disappointment and is sorry that he cannot fully satisfy the club's support, describing himself as "irritated and frustrated" by the situation.
"We were in a position for a long time where our fans thought we could win the league and didn't," he said at his post-match press conference.
"It was a strange atmosphere. Some fans were protesting, yes, but the vast majority were supporting the team.
"I'm sorry if I can't keep everyone 100 per cent happy. I think it is more disappointed love than real aggression.
"We were warned about the protesters. You want to make the fans happy and I'm sorry if I don't achieve it. I'm irritated and frustrated if I cannot keep people happy. I have respect for the club and gave so much for the club.
"Our job is to do the best. This season we hoped we could win the league - it didn't happen and that's why people are frustrated.
"I can share that frustration. The aim is to come back and do what is needed to do it next year. The club has moved forward in the last three years.
"We have Man City now. We have to give a special game next Sunday."
Wenger insisted he does not object to supporters airing their views, but again attempted to reiterate his commitment.
More pictures of the protest
He added to Sky Sports: "We respect the opinion of everybody and we give absolutely the best. I have shown my commitment and care for the club and for the fans.
"I'm really sorry that I cannot make them all happy of course and I will continue to work hard to achieve it."
