Less than 72 hours after their draw with Borussia Monchengladbach in the Champions League, a much-changed City side came from behind to claim three points that took them to the top of the table, for a few hours, before Chelsea beat Tottenham.
Guardiola joked Sergio Aguero's scrappy goals were "beautiful", with the Argentinian again City's hero despite playing through the pain of a minor foot problem.
Dean Marney gave Burnley a deserved lead with a brilliant 25-yard volley, his first Premier League goal for seven years, but Aguero equalised in the 37th minute and then netted the winner on the hour.
"It was a tough week," Guardiola revealed. "Just two days after the Champions League to come here to play. We adapted quite well. Now we have one long week to prepare for Chelsea, Leicester, Watford and Arsenal.
"It's so important our win because it's so complicated to defend. You cannot press because it's long balls, they are taller than us. The second balls, they are really good these kind of teams.
"It's always complicated to control that in these kind of games. Hopefully in the future we can control them better."