Jose Mourinho claimed Manchester City should have been reduced to nine men and said their 3-0 win over Chelsea was a "fake" scoreline.
The Chelsea manager thought that Fernandinho should have been sent off for an elbow, while the Brazilian was only booked, and argued Yaya Toure should have been cautioned twice.
Costa required a bandage to his head after a the first-half clash with Fernandinho and Mourinho said in a news conference: "My feeling? Red card."
He admitted that referee Martin Atkinson's decision to allow Toure to stay on the field had no bearing on the outcome.
"Yaya Toure [should have been a] second yellow but the minute was the 83rd and it was 3-0," he added. "It has no relation with the result but it has a relation with the rules and the rules say [that in] minute one or minute 90, it was a red card."
Mourinho admitted City were the superior side in the first 45 minutes but argued his team were on top thereafter as he insisted the three-goal margin was unfair.
"If the 1-0 was a doubtful result at minute 70, 3-0 is completely fake," he explained. "At 1-0 Chelsea were the best team for the whole second half. After our second half a 1-0 result would be unfair, so imagine the 2-0 or the 3-0.
"They were the best team in the first half. They controlled the game and create chances. We were comfortable with the ball but defensively we were quite fragile. In the second half, everything changed. We brought our defensive line to the midfield line. We pressed them and we created chances. We had lots of space in midfield.
"The second goal was out of context. We were punished for our mistakes for the second and third goal."