However, according to English publication The Sun, the France legend gave Mourinho a call because he was anxious his managerial colleague would think he is plotting behind his back and putting more pressure on his shoulders.
"This game was really bad but everyone has a responsibility for that".
Since then, reports of unrest with leading player Paul Pogba, which led to the Frenchman being demoted as vice-captain, have led o suggestions that Mourinho is losing his influence at Old Trafford.
The Black Country outfit have enjoyed a cracking start to the campaign under the tutorship of Mourinho's fellow countryman Nuno Santo, who has led his troops to an impressive 12 points from seven games, suffering only one defeat in the process.
United fell 3-1 to West Ham on Saturday, the latest in the line of shocking results this season.
Left-back Shaw apologised to supporters for United's "awful" performance at the London Stadium and said the players needed to take a hard look at themselves.
Simon Gleave, head of sports analysis at Gracenote, said: "Manchester United's win against Young Boys was expected but actually having the points on the board has increased the Red Devils' chance of a place in the last-16 from 68% to 84% according to the Euro Club Index".
Ahead of Tuesday's Champions League clash with Valencia, Mourinho insisted he doesn't fear for his job but refused to state whether he had met with the club's executive vice-chairman Ed Woodward in the past few days.
"Ask him", Mourinho said at a news conference on Monday. "We have spoken between us and we know the situation is not good and we can do better".
Tuesday's match at Old Trafford could be a good opportunity for United to bounce back against a Valencia side who have one win in eight matches in all competitions this season, although that came against Real Sociedad on Saturday.
But the Portuguese would not confirm or deny whether Zidane has been in touch about the United job.
Sanchez, who has yet to net in the Premier League this term, is said to have made it clear to everyone behind the scenes that he was unhappy with Mourinho's decision.
United now look far from contenders, but they can take a huge step towards the last 16 by moving six points clear of Valencia in Group H on Tuesday.