A 1-0 victory at Sunderland on Saturday kept the Gunners' hopes of a top-four finish alive, although they remain four points adrift of arch-rivals Tottenham after their 2-1 home win over the Black Cats' neighbours Newcastle.
Wenger's men might have prevailed far more comfortably at the Stadium of Light had it not been for some less than effective finishing and the form of home keeper Simon Mignolet, but the Frenchman admitted afterwards that the three points were all that mattered.
He said: "We were under pressure to win, and of course we could not afford to drop points.
"I said that after the Chelsea game, we are in a situation where we cannot drop points any more. No matter where we play, we need the three points."
Mignolet had already denied Theo Walcott twice and Aaron Ramsey, as well as seeing Olivier Giroud fire across goal, when Santi Cazorla capitalised on good work by Jack Wilshere and Walcott to blast home what would prove to be the winner.
Ramsey would have doubled his side's lead in first half stoppage time had it not been for Mignolet, and the visitors headed for the dressing room knowing the game was theirs for the taking.
However, Sunderland emerged in far more determined mood, and their hopes of salvaging a result increased significantly despite leading scorer Steven Fletcher having earlier wasted a glorious chance to level, when Carl Jenkinson was sent off for a second bookable offence with 28 minutes still to play.
Despite their numerical disadvantage, Arsenal had enough chances to kill the game off with Walcott hitting the post 15 minutes from time, but having failed to do so, they found themselves defending for dear life and keeper Wojciech Szczesny had to make late saves from Fletcher and Adam Johnson.
Wenger was delighted with the way his defence, in which full-back Bacary Sagna had to play at centre-half after Laurent Koscielny hurt himself during the warm-up and was replaced by Jenkinson, coped with the last-gasp assault, but was less pleased with what happened at the other end.
He said: "We lacked efficiency in our finishing, we didn't finish what we created. But we create, and that's positive.
"Sometimes, it's like that. If you look at our games, we score five, seven and suddenly sometimes none, because maybe this team is developing and learning and needs to be a bit more efficient."
For Sunderland, it was a second successive Barclays Premier League defeat and a third league game without a victory, but one which left manager Martin O'Neill and his players wondering just how they had come away with nothing to show for their efforts.
Central defender Titus Bramble said: "It was just one of those games where we could have been there all day and we wouldn't have got the equaliser.
"We tried, we plugged away, but without any success. With the amount of chances we created, on another day, we score three or four goals. But it just wasn't the case.
"As a neutral, I think it was a great game to watch. It was certainly a good game to play in. The only bad thing was the result."
While there were contrasting emotions for the two managers on the final whistle, both were left with fresh injury concerns, although optimistic that they were not particularly serious.
In additions to Koscielny's calf problem - Wenger was confident his absence will be a matter of days rather than weeks - the Gunners boss saw Wilshere limp off five minutes after the break with a thigh injury sustained in a clash with robust Sunderland midfielder Alfred N'Diaye although again, he is hoping his lay-off will be brief.
O'Neill opted to replace skipper Lee Cattermole, making his first start since November on his return from a knee problem, at half-time with a combination of soreness, a lack of match fitness and a second-minute booking taking their toll.
Perhaps more worryingly, left-back Danny Rose suffered a recurrence of the hamstring strain which had previously limited him to one appearance as a substitute since January 5.
O'Neill said: "I think he thinks it's maybe not as bad as the time before. We will asses him again in the next 24 hours, but that was disappointing."