The Spanish forward was caught making the signal after Jamie Vardy and Riyad Mahrez continually tore through the Blues defence.
Jose Mourinho suffered a ninth defeat in 16 matches and admitted afterwards it would now be impossible for Chelsea to qualify for the Champions League.
Sky Sports pundit Jamie Carragher disagrees with Costa's actions though and says it doesn't help the team.
He said: "There's nothing worse than a player coming back and telling other people what they should be doing.
"It's not what he should be doing considering he's been asleep all season."
Chelsea are now a massive 20 points behind the league leaders Leicester and 14 points off Manchester United in fourth.
"The top four is gone - clearly," Mourinho said.
"We were the best team for 20-25 minutes, maybe for a maximum of 30 minutes. They were best team for an hour.
"When some of your players don't hit the levels they are capable of it is hard to see. This season we are doing so bad for some reason, not all of them."
They are also just one point above the relegation zone.
Next up for the Blues is a clash against Sunderland who could go level on points with Mourinho's men if they cause an upset.