The Andalusians' boss was happy with a fine collective performance and praised his side's second-half display
Jose Barkero gave the home side a first-half lead but two goals from Isco meant that los Boquerones left Valencia with three points.
"We knew it was going to be hard to play here. Levante are really good at home and have proved in the past that they can handle our system," said Pellegrini.
"It was a balanced game in the first half, but we improved vastly in the second half. As a group we played well, and individually everyone was on their game."
However, Levante coach Juan Ignacio Martinez was of the belief that his side deserved to win the game and highlighted the impact of Isco as decisive.
"Overall, I think we were better than our opponents. We played well individually and collectively, but we just couldn't take our chances," he added.
"Today has been a bit of a shock to us. We said at half-time that we had to remain tight, but when you are up against a player like Isco, anything can happen."