Chelsea boss Antonio Conte praised the "personality" of his side's performance as the London based club became the first English side to win at Atletico Madrid.
The Blues claimed a last-gasp 2-1 win at Atletico Madrid on Wednesday night to top Champions League Group C with two wins from two games.
Costa, whose return to Atletico was completed on Tuesday, watched on as Chelsea responded from David Luiz's concession of a penalty scored by Antoine Griezmann.
Michy Batshuayi's 94th-minute goal ensured that Conte's men became the first team to beat Atletico at their new Wanda Metropolitano Stadium, after Alvaro Morata's header had cancelled out a first-half penalty from Antoine Griezmann in Wednesday's clash of Group C heavyweights.
Speaking after the game, Conte said, as reported by ESPN: "Our performance was very good and I'm very happy for my players. To play in this way, with this spirit, with this personality, is not simple. You know very well when you go 1-0 down against Atletico Madrid it's very difficult to come back."
"Despite this in the second half we continued to play very well, with great concentration and great personality. We scored twice and we deserved to win."
"We must play always with the same personality, the same desire to play football and to try through the play to deserve to win. And the answer tonight was very positive," said Conte, according to Sky Sports.
Atletico boss Diego Simeone conceded his side were second best, saying: "Chelsea were the better team. The draw was a good result for us, but at the very end they had the patience to move the ball round very well and scored at the last second.
"They had better intensity, they were better at a tactical level. We were never comfortable. It was a fair victory for Chelsea because they just played better," Simeone said.
The result sees Chelsea maintain their two-point lead over Roma at the top of the group, but after the match Conte was torn between elation at the result and anxiety at a lack of preparation time for the visit of Premier League title rivals City to Stamford Bridge.
Eden Hazard was in scintillating form for Chelsea, hitting the post with a shot from distance and crossing for Morata to score, and Conte was full of praise for the Belgian.
"Eden's performance was amazing," he added. "It was the first big game for him after the bad injury and his answer was fantastic. He had a great link with Alvaro."