The Spain international appeared as a second-half substitute in the Premier League clash at the King Power Stadium, in which the 10-man hosts snatched a 94th-minute equaliser to deny United the win.
The goal came after United defender Chris Smalling was sent back into the heart of defence despite having required treatment for a groin injury in the closing stages, and it was his inability to meet Marc Albrighton's cross that allowed Harry Maguire the chance to score.
Former Red Devils captain Gary Neville later accused Herrera of refusing a call from team-mate Phil Jones to slot in at right-back as part of a reshuffle to cope with Smalling's injury.
Herrera appears to have responded to the criticism with a cryptic Twitter post on Christmas Eve.
"Happy Christmas to everyone, including the ones that try to invent stories that never happened," the 28-year-old wrote.
Neville, speaking on his podcast, had said: "Smalling has got to flag up as an experienced defender that he's struggling, get someone else into the centre. It didn't happen for two or three minutes.
"Then Phil Jones recognised it had happened and tried to reorganise – as I saw it, Ander Herrera refused to go to right-back and told Henrik Mkhitaryan to go back there.
"All over a sudden Smalling sits down on the floor and then goes off the pitch and then comes back on at centre-back. He ends up picking up Harry Maguire.
"You can’t believe the disorganisation and lack of leadership shown by Manchester United at the end of that game in a game they should have won. Jose [Mourinho] will be furious when he watches that back."
Manager Mourinho accused his players afterwards of a "childish" approach to the game as they failed to hold on to the 2-1 lead given to them by Juan Mata's fine double.