The Citizens went ahead through Danilo's long-range effort on 22 minutes but despite dominating the encounter could not add a second.
Burnley eventually made the visitors pay as Johann Berg Gudmundsson equalised with a half-volley eight minutes from time.
"Of course we are frustrated in terms of the result but the performance was outstanding against a Burnley side who are the most British of teams in terms of long balls and the way they play," Guardiola told Sky Sports News.
"But football is about goals. We needed to score the second, third and fourth when we had the chance. When you arrive in the last 15 minutes at Burnley 1-0, this is what can happen. I'm sad for the players because we played so well.
"What they have done this season, Burnley, is amazing. We controlled the game, but when we arrived in the last minutes at 1-0, there is danger."
City return to action next Saturday with a Premier League home game against Leicester City.