Diego Simeone's side going into the game as favourites defeated Barcelona 2-0 to keep their hopes of defending the title alive.
Suarez punished his former side with Atleti's second goal of the night after Thomas Lemar had opened the scoring in the 23rd minute.
Following the arrival of Koeman at Barcelona, the Dutch trainer reportedly told Suarez he was surplus to requirements at Barcelona through a 60-second phone call.
And after scoring in yesterday's game, the Uruguayan forward gave a controversial phone call celebration which was said to be a dig at Koeman but the former Liverpool man has denied the reports.
"It was for the people who know I have the same number, so they know I'm still on my phone,” he said.
"It was something I had agreed on with my kids."
After the celebration, Suarez also clasped his hands together in prayer with his eyes closed, a way of asking Barcelona fans for forgiveness.
The 34-year-old has never been happy with how he was kicked out of Barcelona, pouring out his frustration in February, Suarez said;
"When Barcelona told me that they did not count on me it was hard, I did not expect it,” he said at the time.
"They were very difficult moments because of the manner [in which it happened].
"Koeman called me and told me that I was not in his plans.
“When Barcelona made it official that they did not count on me, conversations began with Atleti, with Cholo [manager Diego Simeone], with [CEO] Miguel Angel."
Atletico Madrid are now second in the league log with 17 points after 8 games.
