Xavi, who made his 392nd Liga appearance to break a club record, decided the game with a terrific free kick against the hosts, who would have Jaime and Dani Benitez dismissed.
"We were lucky to have won," Guardiola is quoted as saying by Sport.es.
"Anything could have happened at 1-0 as they have dangerous players.
"We were not fast enough in moving the ball around. We would take four or five touches before playing it on. We are usually strong at this.
"In any case I felt we were in command of the game."
Javier Mascherano, however, believes his side were deserving of victory.
"I think the team has taken three deserved points," added the Argentine.
"We knew Granada would be a difficult rival, but we had chances and we were able to finish.
"The win was deserved and what is important is that we were able to create plenty of openings."
The victory took Barcelona back to the top of the table, but if Real Madrid or Levante win on Wednesday evening, the Catalans will be knocked off the summit.
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