City were 2-0 down to the Championship side at half-time in the FA Cup fourth-round tie at the Etihad Stadium.
They eventually rallied to win 4-2 after a Sergio Aguero hat-trick and Pellegrini wants his side to heed the warning as they prepare to take on Tottenham at White Hart Lane on Wednesday.
Pellegrini said: "It was a good lesson - to pay attention in the right moments.
"In football the difference between winning and losing is very slight.
"I can't say what they saw of me, but I think we made the correct arrangements during half-time.
"I think the reaction was very important, as was the way we finished the game."
City thrashed Spurs 6-0 when the sides met in Manchester in November, but the Londoners have found form under new manager Tim Sherwood and have won five of their last seven.
Pellegrini said: "The results say that they have improved a lot.
"They have won the last four (Premier League) games. I saw the last two games they played and they are playing very well."
The match also brings City up against their former player Emmanuel Adebayor, whose game has been revived under Sherwood with three goals this month after he was frozen out by former manager Andre Villas-Boas.
Pellegrini said: "It is always important to have a striker Adebayor in a good moment so I am sure we are going to have a very tough game against them.
"It is important I know that our team will try to go there and win the game, not the history with him."