Two defensive blunders from Sporting helped Atletico to a simple win, with Koke netting in the first minute before Antoine Griezmann raced through on goal to double their lead shortly before half-time.
However, despite Costa not getting on the scoresheet, Simeone singled out the Spain international for praise after the game.
He said, as quoted by Mundo Deportivo: "Since he came back, it's the best match he played. He was an animal, ran to everything, diagonals, participated in the goals, pressed. It is the best match since he returned."
Atletico's games don't get any easier, with the Madrid derby next to come at the weekend, but Simeone insisted his side will be ready to play Real despite their European tie coming two days later than their rivals' Champions League game.
He added: "The team at the end suffered the tremendous wear and tear throughout the game. It is logical, having pushed as the team pushed. There is no excuse for Sunday, we will be fine, as always.
"The game was clear. The greatest danger appeared from the loss of the opponent's balls. The two teams are similar in that sense. The match was raised in a similar way. The talent of Griezmann and Koke took the match to our side."
When asked about Atletico's favourite tag for the Europa League, Simeone said: "We live from day to day. We depend on the match of Madrid to keep second place and get closer to Barcelona, then we will play the round. Here the facts count, and it will depend on what we do in Lisbon on Thursday.
"I always say that glasses are dangerous, you're never calm, we've seen thousands of situations. The 2-0 is important as long as we go out for the game as we did here.
"Look what we did in [Lokomotiv] Moscow, that speaks for itself. I do not underestimate anyone or imagine anything."