The controversial former England batsman was out for five as Perth Scorchers fast bowler Mitchell Johnson put on a scintillating display in the match on Tuesday.
The Western Australia side won by seven wickets to take the Scorchers into a home final this weekend, while Pietersen departed the field during their innings with a hamstring injury.
"Time for Stars to move KP on, spent to much money on him and didn't win. Don't want to listen to his excuses anymore," Lehmann tweeted after the match.
Pietersen, 36, did not respond to Lehmann's remarks, instead tweeting that he was "Gutted with this eve! Sorry @StarsBBL fans!"
Stars president Eddie McGuire hit back at Lehmann on radio Wednesday, saying: "KP is not the highest paid player at the Stars for a start, he has delivered is spades.
"The last three Big Bash leagues, KP is second only to (Brisbane Heat's) Chris Lynn for runs scored. He has bought in that many people," he said on commercial radio station Triple M.
"The last two years which team has had the biggest crowds in the history of the Twenty20 Big Bash. He is a crowd favourite."
Pietersen last week criticised Cricket Australia for not releasing teammate Marcus Stoinis for last Saturday's clash against the Sydney Sixers.
"I just find it bitterly disappointing that a guy can't play in a fixture tomorrow, which is a big fixture for us. He will be sitting in a hotel room," the Sydney Morning Herald reported him as saying.
"Stoinis might not play (the one-day international against Pakistan) on Sunday, he certainly would play for us tomorrow (Saturday)."
Stoinis did not play for Australia on Sunday, while the Stars lost to the Sixers on Saturday.
BBLBig Bash Leaguecricketcricket newsDarren LehmannKevin PietersenMelbourne StarsTwenty20 Big Bash League
First Published: January 25, 2017, 1:43 PM IST