Eden Hazard's brace secured the Blues a 2-1 win against Pep Guardiola's men on Wednesday evening, pushing Antonio Conte's men closer to the Premier League crown.
There had been suggestions Costa could miss a chunk of the run-in after appearing to kick out at City defender Kompany, but the striker will not face any sanction.
Referee Mike Dean saw the second-half incident and dealt with it at the time, meaning there will not be any retrospective FA action.
Neither Chelsea boss Conte nor City counterpart Guardiola saw Costa catch Vincent Kompany with his studs in midfield.
"I didn't see it, but during the game it's very difficult," Conte said
"Yes, you see this kind of contact but it's impossible to tell, to judge this kind of contact."
Source : PA
Source: PA