The midfielder’s brother hammered Rangnick for denying the player a final run-out at Old Trafford in their last home game before his contract expires in the summer.
However, Rangnick has insisted that he could only bring on one of Lingard and fellow out-of-contract star Edinson Cavani, having also wanted to play youngster Alejandro Garnacho.
“To start with, in the last couple of weeks under my tenure he has played far more games than he used to,” stated Rangnick on Friday.
“Secondly, on the day of the game against Chelsea he asked me to release him from the game and training the following day for personal family reasons. And this was the reason.
“With only three substitutes I had to take a decision between Edinson Cavani and Jesse Lingard, or the young [Garnacho], who I would have loved to have brought on and given a chance to play.
“I took the decision to bring on Edinson. Had I not brought on Edinson someone else might have asked if it’s classless not to bring on Cavani or Garnacho.
“You have to take a decision and this will not be to the liking of everybody and this is part of the game.”
United round off their campaign away to Brighton and Crystal Palace, with Marcus Rashford ruled out of Saturday’s trip to the Amex Stadium.