Following the loss to Atletico, Martinez said he expected more investment in the Manchester United squad and “more from our technical director [Jason Wilcox]”.
He later said he “spoke out of anger and frustration” in making those comments and that he had “belief in my team-mates, our manager and everyone working to help this club move forward”.
Former Manchester United captain Roy Keane, speaking on The Overlap podcast, described the situation at his former club as “a bit of a circus”.
“Our club is at its best when we are all united, and I recognise that my words in that moment did not help with that,” added Martinez on Thursday.
“I know that every single person at Manchester United is doing everything possible to achieve our shared ambition: bringing the success that this club and its supporters deserve.
“With this situation now behind us, we are fully focused on winning together.”
It remains to be seen whether Carrick selects Martinez for the trip to Leeds.
Nevertheless, there is understood to be significant doubt over Martinez’s long-term future at Old Trafford.
His current deal expires at the end of the season but the club have the option of extending the contract by 12 months.
While the issue over his recent comments is now considered closed, the club are still to decide whether they want to trigger the contract option.
