Television cameras captured the Portuguese coach muttering what are reported to have been profanities in his native tongue as he headed for the tunnel following his side's second-half turnaround, which saw them fight back from 2-0 down to take all three points.
The FA confirmed on Monday that Mourinho will be investigated over the incident.
Mourinho, appointed United manager in May 2016, had been the subject of intense speculation in the build-up to the game with one UK newspaper reporting he faced the sack regardless of the result.
Second-half goals from Juan Mata, Anthony Martial and Alexis Sanchez ensured United avoided a fourth Premier League loss of the season and Mourinho spoke afterwards about the effect of "the pressure of man-hunting" on his players.
The Old Trafford boss said: "As a friend of mine was saying to me this morning: if tomorrow it is raining in London it is my fault.
"If there is some difficulty to have the agreement of Brexit, it is my fault. And I have to be ready for this.
"I think a lot of wickedness and a clear man-hunting which I think in football is too much.
"It is a life I love, it is the life I worked for since I was a kid and I will love this until my last day. It is one more thing in my life."
Former Utd defender Rio Ferdinand took issue with the manager's comments, however, stating: "I don’t know where ‘wickedness’ and ‘manhunt’ come from.
"Because if you see something on the football pitch, you talk about it. He’s the Manchester United manager. Man United’s manager doesn’t go unnoticed - win, lose or draw. There’s going to be scrutiny.
"You say what you see, you can’t expect anything different. And to sit and moan and [say] ‘oh they’re hunting me’ and ‘it’s wickedness’ … I find it laughable."
The visit of Newcastle followed a run of four games without a win in all competitions for the Red Devils, who suffered defeats to West Ham in the Premier League and Derby County in the EFL Cup during that spell.
United's next game sees them face Mourinho's former club Chelsea in the Premier League at Stamford Bridge on October 20.