Drinkwater caught Ramsey with a late tackle in the 72nd minute and was lucky to escape punishment at Emirates Stadium.
Replays showed the reckless nature of the challenge, with Drinkwater catching the Arsenal star high on his right leg.
However, Ramsey commented on a photo about the incident on Instagram to reveal that Drinkwater was quick to say sorry after the final whistle.
The caption on the photo above read: “And you get criticised for rolling on the floor…. Very poorly timed challenge, you did well to get up from that one @aaronramsey. #wow #crikey #rambowouldbeproud #arsenal #leicestercity #greatgame #controversy”
And Ramsey replied: “Yes @the_baldwinners, was a sore one but credit to him, apologised straight after the game.”
Danny Welbeck scored Arsenal’s stoppage-time winner as the north London side came from a goal down to earn all three points against the Premier League leaders.
Jamie Vardy had given his side the lead from the penalty spot in the first half but substitute Theo Walcott equalised for the Gunners, before Welbeck glanced Mesut Ozil’s free-kick home deep into stoppage time.
MORE: The latest football news