But despite righting the ship at Burnley and a two-week global break to ease the pressure, Mourinho again took aim at the press.
Rashford, who is suspended for Saturday's trip to Watford, scored twice for England during the global break prompting suggestions he should be play more regularly for his club.
At his pre-match press conference ahead of United's trip to Watford in the Premier League, Mourinho saw the amusing side of the incident and joked he would have been penalised on the pitch.
Everton were interested in signing Marcus Rashford from Manchester United in the summer transfer window.
Some of them, they have a problem with some compulsive lies, so I can expect that Sunday some of them they will wake up in the morning and as always the first thing they think is José Mourinho.
'Performances with England, of course I'm happy, he played well, competed well, he score and especially in a period where he comes with some sadness after his suspension and it was very good that he did that.
As a former striker himself, Lineker has seen Rashford's stagnating development at Manchester United through sympathetic eyes.
"It's not my business to interfere with club managers, they have a hard job to do and they have big squads at the top six, huge competition for places, so Jose thinks the world of Marcus", Southgate said. If you want to divide that by 90 then it is 34.2 matches of 90 minutes in 16-17.
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"In 17-18, he played 35 Premier League matches, eight in Champions League, five in FA Cup including the final, three League Cup matches and the European Super Cup final".
"So with me, in two seasons, he had 105 appearances, 5774 mins, 63.7 matches of 90 mins, including five finals, so the people that is speaking about these minutes, I think they are a bit confused".
Rashford was a second-half substitute against Brighton, didn't come off the bench in the 3-0 home loss to Tottenham, and entered as a 61st-minute substitute against Burnley only to be red-carded 10 minutes later.
Daily Telegraph columnist Jamie Carragher made the point that Rashford has the most hard of tasks at United - a young player coming through as a striker at a big club.
However, should regular game time be hard to come by for Rashford at United, he may be forced to consider a move in the future.
The Manchester-born striker has been in and out of the United starting XI ever since Jose Mourinho became manager in 2016, but Southgate insists the Portuguese coach is a "huge admirer".
Ruben Loftus-Cheek is another of England's squad that advanced to the semi-finals of the World Cup struggling for minutes at Chelsea.
Chelsea's Loftus-Cheek, 22, has managed 2,341 minutes, and that includes his spell on loan at Crystal Palace.