An FA Cup humbling at the hands of Championship side Blackburn Rovers and a UEFA Champions League mauling by Bayern Munich had heightened tensions in and around the Arsenal camp heading into the weekend.
The Gunners were, however, able to collect a third consecutive Premier League success as Santi Cazorla struck twice against Villa to lift the Gunners to within a point of the top four.
"I am relieved, of course, because it was important to get the three points today," Wenger told Sky Sports afterwards.
"We are on a good run in the Premiership. We were affected by our two major disappointments we had, you could see that on the nervous side, but we have a good spirit in this team and they were focused and determined.
"Even when it came back to 1-1, we found the resources to win the game. We could have scored many, many more goals today, but the most important thing was to get the three points.
"In the last 12 games in the Premiership, we lost two - one was against Man City with 10 men from the start and one at Chelsea. We are on a positive run and let's continue that."
Wenger saw Cazorla break the deadlock with just six minutes on the clock, and he concedes that it was important for Arsenal to start positively in front of a disgruntled Emirates support.
He added: "It was very important.
"The fans were great. Our fans are intelligent and know that we are in the battle to get as close as possible to the top and that we need their support.
"No matter how disappointed you are after the Bayern Munich game, what is important is to stick together and get the points and the wins.
"It has been a very demanding week physically and nervously and it was important not to feel sorry for yourself. We responded in a strong way today."
Meanwhile, Wenger is waiting on an update regarding the problem which forced the unfortunate Abou Diaby from the field just after the hour mark.
On the French midfielder, who has suffered countless injuries during his time in England, the Gunners boss said: "He told me he got kicked on the hip after he felt his calf. I don't know how bad it is."