The Uruguayan -- who moved to Barcelona from Liverpool -- struck twice in the first-half yesterday to give his side the upper hand heading towards the second leg at the Nou Camp next month.
Sergio Aguero grabbed a goal for City -- though the hosts were soon afterwards reduced to 10 men when Gael Clichy was sent off -- and Joe Hart kept City in it with a last minute penalty save from Lionel Messi.
Suarez, who took his tally to nine goals for Barcelona in 23 appearances in all competitions, admitted Hart's save had kept the tie alive.
"I think that is a positive thing for them," said Suarez, whose career at Barcelona started belatedly as he served a suspension for biting Italian defender Giorgio Chiellini in last year's World Cup.
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"If it had gone in it would have been a different scenario.
"But at 2-1 there's a chance for them."
"We conceded an early goal and played very bad. In the second half we did what we talked about before the game," said Pellegrini.
"We have a chance. We must try to do it there in the next game.