Costa stood on the ankles of Emre Can and Martin Skrtel during the match at Stamford Bridge and Rodgers claimed the Spain international striker could have avoided the contact, insisting the former Atletico Madrid man was lucky to avoid a red card.
Skrtel and Costa clashed numerous other times, while the Brazil-born forward went head-to-head with Liverpool Steven Gerrard as well, having had an altercation with Jordan Henderson in the first leg.
Chelsea triumphed 1-0 after extra-time in a tense contest on Tuesday, knocking off Liverpool 2-1 on aggregate to reach the League Cup final.
"These things happen in the game but I think anyone watching it would not like to see what we've seen Diego Costa do," Rodgers told Sky Sports.
"Not just on Martin Skrtel but on Emre Can, a young player who was clearly stamped on.
"You don't want to see that. There's no need for it. You can easily land somewhere else without having to directly land on an opponent's ankle.
"It's disappointing to see that on the replay and he [Costa] was probably very fortunate the referee and the linesman didn't see it."
Chelsea manager Jose Mourinho was also not happy with some non-decisions by referee Michael Oliver in London.
The home side appeared to be denied a penalty in the first half, while Henderson looked fortunate to escape a second yellow card after half-time when he stopped a Chelsea attack with his hand.
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