Torres was left with a simple finish following a miscommunication between Matija Nastasic and Joe Hart in the 90th minute, which saw the defender head the ball beyond his goalkeeper.
Chelsea had earlier been pegged back by Sergio Aguero's equaliser after Andre Schurrle had broken the deadlock, and Torres felt the three points were fully deserved.
"When you win a game like this against a great team like Manchester City in the last minutes of the game it feels much better," Torres told Sky Sports.
"I think 1-1 was not right for the game. I think we controlled most of the game and we had more chances in the first half.
"At the end we won a game we decided to win. We are happy because it is our first win against a contender for the Premier League."
Torres, who set up Schurrle's opener, grabbed the winner from what was little more than a hopeful punt forward.
"You never know which ball can be the most important in the game," Torres said.
"A long ball just looking not too complicated, but (it was) not the best understanding between the defender and the keeper. You win the game in that action."
Torres could have had a goal before then as he blazed over with only Hart to beat with the game scoreless, before crashing a shot against the crossbar at 1-0.
"I was unlucky to miss the chance that I missed in the first half. I thought I was offside - I should have stayed more calm," he said.
"I missed the chance but then in the next action I got the assist for Andre and then I hit the post.
"I'm really happy for the team and my performance. The team is showing it is improving and that is very positive."