Costa, who also had run-ins with Martin Skrtel and Steven Gerrard in what was a bad-tempered match on Tuesday nightg, appeared to stamp on Emre Can during the first half but referee Michael Oliver took no action against the Spain international.
And Rodgers, whose side lost 1-0 on the night and 2-1 on aggregate, was disappointed with Costa???s actions, claiming there is no place for it in football.
“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 was probably very fortunate the referee and the linesman didn???t see it.”
Despite the defeat, Rodgers was full of praise for his team???s performance and singled out Chelsea goalkeeper Thibaut Courtois as the difference between the two sides.
“We???re very proud of the team,” he added.
“Over the two legs, we were the better side but their goalkeeper has got them to the final.
“Up at Anfield and here tonight, he???s made some very important saves and that???s won them the game.”
On a brighter note, Rodgers revealed Daniel Sturridge could return to the Liverpool squad when they host West Ham on Saturday.
“Obviously it was too soon for this game but I think he???s really relishing coming into the team,” said the Reds boss.
“The team???s playing with confidence now and you put him in this side and it lights it up even more.
“He???s worked very hard to get back and he???s training with the team. This was game was too close for him but by the weekend hopefully he can play some part.”