Influential midfielder Nasri picked up a hamstring injury in the 2-1 FA Cup fourth-round win over League One Huddersfield at The Emirates on Sunday.
The Gunners made sweeping changes from the side which had booked a place at Wembley with their midweek Carling Cup semi-final second leg win over Ipswich.
However, because of concerns over the fitness of Tomas Rosicky, who has been troubled by a virus, Wenger elected to put Nasri in the starting XI.
It had all been going to plan when Nicklas Bendtner's angled shot deflected in off Terriers skipper Peter Clarke to put the Gunners ahead on 22 minutes.
However, French playmaker Nasri then limped off with a hamstring problem as he chased a long kick up field from Manuel Almunia.
Wenger said: "Nasri looks to have a serious hamstring injury. Usually it is three weeks.
"We have to see if it is a grade 1, it will be two weeks, so we will see.
"I have now regrets because the plan was to play Rosicky, but he was still too weak because he was sick, so I took the gamble on Nasri.
"It backfired, but he could have come on and that happened as well.
"It is very difficult to predict. We are at the stage of the season where we play so many games that to lose bodies is very difficult for us.
"But Samir is a big blow."
Sebastien Squillaci was shown a red card by referee Mark Clattenburg for blocking Jack Hunt's surging run just before half-time.
Alan Lee headed a deserved equaliser for the Terriers, but captain Cesc Fabregas came off the bench and won it from the spot after Jamie McCombe was adjudged to have pushed Bendtner over.
Arsenal had also struggled to get past Leeds here in the third round, when Fabregas also netted a late penalty to earn a replay which the Gunners went on to win comfortably.
Wenger accepted Huddersfield had given his battle-weary players a great test of character.
"It was tough, tough, tough and had all the ingredients of a typical cup tie," Wenger said. "I think we played a bit below par, and Huddersfield are a good team - they were efficient, dangerous on set-pieces and crosses.
"We were also down to 10 men and so it became of course very difficult.
"In the end, though, we had the quality to make a difference, but we play so many games at the moment that of course sometimes we are not as sharp as you want to be."
Wenger felt the red card for Squillaci, just back from a hamstring injury, was "harsh".
The Arsenal manager said: "You can give it and not give it. It was a foul, but it didn't look to me that it was an obvious goalscoring opportunity.
"Is he the last man? That I am not sure as well. I feared the red card and unfortunately he gave what I feared."
Fabregas, who was sent on in the second half, appeared to gesture to the referee for a red card as further punishment at the penalty.
Wenger, though, maintained: "Cesc thought it was a red card. It is for the referee to make the decision. He made the right decision in my opinion.
"In the box, personally I am more lenient than outside."
Arsenal appear unlikely to sign anybody ahead of the transfer deadline.
Wenger said: "I will leave the headlines to other clubs. But I cannot tell you definitely no because if somebody knocks at my door in the morning and says 'I would like to play for you' and he is a good player, I will sign him."
Arsenal have little time for any tired legs to recover as they host Everton in the Premier League on Tuesday night.
"We looked a little bit tired. Hopefully we can recover," Wenger said. "When you win you recover more quickly.
"I have some players who did not play who will be fresh, but we have only 48 hours."
Terriers boss Lee Clark revealed pride at his team's efforts and challenged them to now go on and secure promotion to the Championship.
"It was an excellent performance - we passed the ball well and created chances," he said. "We limited Arsenal, which is not easy coming here, and the lads have worked extremely well so that in context we are disappointed we did not get anything more from the game.
"But we have now go to look at our league programme, which is all-important for us.
"Our goal will now be to go and get promoted and take this performance into the league."
Clark refused to be drawn on the penalty incident.
"I have not seen it since but from where I was standing in the dug-out, it looked a penalty," the former Newcastle midfielder said.
"Other people have said it wasn't, but from my position it looked a penalty.
"But it is given so you can't do anything about it."