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 whose goal came from Colin Kazim-Richards.
"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."
Rovers boss Michael Appleton hailed his side's achievement as the "highest point" of his short managerial career.
"To come to Arsenal and get through a cup tie is one thing, but to keep a clean sheet and defend as well as we did is another, and that is testament to our players. We have two man-mountains in the centre of defence," he said.
"We had a feeling they might rest a few of their players because they have a big game on Tuesday in the Champions League. However, regardless of what side they were going to put out, we knew we would concede a lot of possession at times, but we are happy with that.
"We have a mentality now where we are hard to beat, and are resilient. It has been almost getting into the heads of the players to take pride in keeping clean sheets and enjoy defending, which people do not like doing at times, we also have a bit of quality as well."