The Gunners face Bayern Munich in the Champions League on Tuesday night and Wenger had made several changes, with Jack Wilshere, Theo Walcott and Santi Cazorla all starting on the bench.
Even so there should still have been enough quality to see off the npower Championship side, with Gervinho missing a great chance at the end of the first half and Abou Diaby's goalbound header saved by Rovers goalkeeper Jake Kean.
Czech winger Tomas Rosicky crashed a 25-yard effort against the bar and then moments after Wenger had made a treble substitution, Rovers snatched the lead after 72 minutes through Colin Kazim-Richards' scrappy effort after Wojciech Szczesny had parried Martin Olsson's shot.
Arsenal pressed for an equaliser and Kean somehow saved a close-range header from Walcott before Olivier Giroud's effort in stoppage-time was blocked as Rovers clung on for a famous win.
The defeat was a first against lower-league opposition in the FA Cup for Wenger, who also saw his team beaten on penalties in the Capital One Cup quarter-finals at npower League Two Bradford.
"We had 11 international players on the pitch at the start of the game. We had a lot of the ball and [Blackburn] defended well. We had 16 shots at goal, they only had one shot at goal," he said. "We made a massive mistake on the goal and we were not good enough to win the game, it is as simple as that. Not one defeat is acceptable. You are in this job to win every single game."
Arsenal now face the possibility of an eighth season without silverware, unless they can come through in the Champions League. The home fans vented their frustrations as boos rang out around the Emirates Stadium at the final whistle.
"You do not want your fans to be happy when you lose at home to Blackburn when the team has one shot at goal," Wenger said. "It is very painful and very disappointing to lose a game like that. What is important now is to focus on the next one."
Wenger added: "The season is not over. For you maybe, not for me. If we feel sorry for ourselves we would be completely wrong. We have a massive game on Tuesday night and we have to show that we some response in the team."