The Gunners' campaign suffered another setback when although dominating Blackburn at the Emirates Stadium, they were knocked out by a scrappy second-half goal from former Arsenal trainee Colin Kazim-Richards.
Despite Sunday morning's negative headlines and criticism of his team selection - which saw Jack Wilshere, Theo Walcott and Santi Cazorla all start on the bench - Wenger insists how his men now respond will go on to define the outcome of what has been one of the most testing seasons of his time in charge.
"You can take a distance in terms of what people say and show how strong and good you are in the next game," said Wenger, who suffered defeat against lower league opposition in the FA Cup for the first time.
"It is a good opportunity to show that we have character and are men who can fight for each other."
Arsenal were also knocked out of the Capital One Cup in a match they had been expected to win when losing at npower League One Bradford on penalties in December.
Wenger, though, maintains he had not taken Saturday's clash lightly, despite what lay ahead in Europe next week.
"It is very disappointing that the two (cup defeats) have happened in the same season, but I prepared these two in the same way that I did in the 16 years before," he said.
"I couldn't see how we could lose this game because we always had the ball and they had one shot on goal, but they defended well.
"It was the kind of game you can lose if you make a mistake at the back and that's what we did. We gave them the game, basically."
Yet even with all of Arsenal's changes, there was still enough quality on the pitch to have seen off the challenge of Rovers, who are battling to get themselves back into the top flight under Michael Appleton.
Abou Diaby's goalbound header was saved by Rovers goalkeeper Jake Kean before, in what proved the match's pivotal moment, Ivory Coast forward Gervinho - making his first appearance after the African Nations Cup - rolled the ball wide of the post when put clear into the penalty area.
Czech winger Tomas Rosicky saw his 25-yard effort come back off the crossbar before Wenger made a treble substitution in an attempt to spark new life into the tie.
However, moments after the change, Rovers snatched the lead after 72 minutes when goalkeeper Wojciech Szczesny parried Martin Olsson's shot back to Kazim-Richards, whose rebound effort bounced up off the ground, onto the post and in.
Arsenal at least had more urgency, but still lacked any real penetration as Kean produced another good reaction save from a close-range header by Walcott while Blackburn's resilient defending was rewarded after Olivier Giroud's blocked effort in stoppage-time was quickly followed by the final whistle.
Rovers were rank outsiders, as long as 11/1 shots to record an unlikely victory.
There will, though, be little time for Appleton - in charge of his third club this season - and the Blackburn squad to revel in their moment of FA Cup history.
"What we have to do very quickly is to move on because we have a (Championship) game against Hull on Tuesday night, which is almost a reality check," said Appleton, whose side are six points off the play-offs in eighth.
"It is our bread and butter, what we will be doing for 46 games across the season, so that is my job and my staff, to make sure we can get that over to the players."
Rovers captain Scott Dann feels the result was testament to the hard work put in by Appleton since his arrival from Blackpool just five weeks ago.
"In the last 18 months there has been too much going on behind the scenes with managers coming and managers going back out not too long after," the defender said.
"What we needed was a bit of stability and the new manager has given us that.
"The way that they have turned things around and got us playing at the moment, we are going from strength to strength."