With time slipping away at the Emirates Stadium on Wednesday, Wenger threw on Danny Welbeck and Olivier Giroud to finish with four strikers on the pitch.
His side eventually prevailed courtesy of a late own goal by Robert Huth.
Arsenal remain outside the Champions League places, but Wenger said: "We have one advantage – the advantage of clarity.
"We have to win our games, so that's why we cannot be happy with a 0-0.
"We absolutely have to take a gamble to try and win the game at any cost. We took the initiative tonight."
With only 72 hours to recover from Sunday's gruelling FA Cup semi-final extra-time victory over Manchester City, Wenger praised the resilience of his players.
"We lacked penetration and a change of pace," he told reporters.
"You could see that we had some heavy legs and we lacked a bit of speed in our game to get Leicester out of position.
"They defend well, but in the end I think the win rewards the team which took the initiative during the game.
"Let's not forget as well that we played on Sunday afternoon. Leicester didn't play at all over the weekend, so we knew we had a little handicap on that front."
Wenger promised Arsenal will approach Sunday's north London derby at Tottenham Hotspur purely as another step towards Champions League qualification, not a chance to halt their rivals' title charge.
"We play for us," said the Frenchman, whose future at Arsenal remains up in the air.
"In life you work for your own achievements, not for those of others."
Wenger played down a touchline incident between Alexis Sanchez and Christian Fuchs that occurred shortly after Nacho Monreal's wayward 85th-minute shot had deflected in off Huth for the decisive goal.
Sanchez twice prevented Fuchs from taking a long throw-in by standing too close to the touchline.
Infuriated, Leicester's Austria international threw the ball into Sanchez's shoulder, only for the Chilean to fall to the ground clutching his face.
Wenger said: "I think Alexis didn't know that he had to be further away. As well, the referee didn't tell him that he had to move away so he thought he was in the right position.
"He got the yellow card because he didn't respect the rules. I accept that.
"But on top of that, Fuchs was lucky not to get a yellow card because he threw the ball at him on purpose.
"If you know Alexis, he doesn't worry about what happens on the pitch. He will be the same tomorrow and on Sunday."
Leicester manager Craig Shakespeare also refused to condemn Sanchez's histrionics.
He was more concerned by a late defeat that means his side remain closer to the relegation zone than is comfortable.
"I think Christian was well entitled to take the throw-in, but we're in the referee's hands for that," said Shakespeare, whose side remain six points above the relegation places.
"It is down to Arsenal to deal with Sanchez. It would be wrong of me to talk about other players. I need to concentrate on my own players and leave Arsene to deal with his own players."
Reflecting on the game, he added: "We defended really resiliently for 85 minutes and we had to against a very good side in Arsenal.
"We'd like to have attacked a bit more, but to lose in the manner that we did is very, very disappointing.
"It was a cruel deflection because the shot wasn't even on target. It happened so quickly that Robert couldn't get out of the way.
"We have to recover quickly from this because we've got another tough away game at West Brom on Saturday."