The two La Liga high-fliers met in the first leg of a quarter-final encounter on Tuesday, and the visitors appeared set to take a one-goal advantage back to Vicente Calderon thanks to Diego's 25-yard screamer in the second half.
However, Brazil international Neymar ensured next week's return fixture will begin with the score reading 1-1, collecting a sublime throughball from Andres Iniesta before finding the net with a curled finish.
Diego had started the game on the bench but replaced forward Diego Costa, who had to depart early due to an apparent hamstring complaint.
Simeone paid tribute to the midfielder and felt both sides deserved credit for the way they approached the tie.
"I'm really happy for Diego and for the goal he scored. He needed that. He came on at a very important moment." said Simeone.
"It was a beautiful game. Each team played to their strengths and stayed true to their style."
Atletico - who currently lead reigning champions Barcelona by one point at the top of La Liga - will have the advantage of an away goal for the return leg.
Midfielder Tiago expressed satisfaction at Atleti's display, but believes Gerardo Martino's men remain favourites to reach the semi-finals.
"The result is a brilliant one for us," said Tiago. "Barcelona are still favourites but we will be at home and will have our chances there. We are going to give everything.
He added on Tele Deporte: "We worked hard. Barcelona have great quality.
"But we believe we played a great game. We're all really excited now to go back to the Calderon and give our all."
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