City failed to add to Danilo's first-half screamer at Turf Moor and were pegged back by Johann Berg Gudmundsson's goal in the 82nd minute.
Sterling has scored 19 goals in what has generally been a superlative season thus far, and Kompany's first response when asked about the attacker's misses was to offer a booming laugh.
The City captain went on to tell Sky Sports: "He's been incredible for us. He's scored more last-minute goals than anyone in this league I think.
"Today it just didn't quite happen, but I give top marks to everyone for effort. I give top marks to everyone for the way we played this game and handled a really tough away game.
"Keep playing like we are at the moment and we'll win more often than not."
City are just eight wins away from a third Premier League title, despite being held by the Clarets.
Guardiola's side have left the rest of the division in their wake this term, but Kompany was clear that they are not taking anyone lightly.
"We never doubted that this league was competitive and we were warned for this kind of situation," he added.
"We knew we'd have to take our chances, I think we did extremely well in this game. We created so many chances, we created some chances in an incredible manner but then we probably ran out of steam a little bit because we kept trying and trying and trying and in the end we get punished for it.
"We don't have to feel too sad about this, our performance was good."