With just three games played, United already find themselves six points behind Liverpool and local rivals Manchester City.
Sources insisted Woodward and the Glazer family, the club's owners, have given no consideration to replacing Mourinho with Zinedine Zidane despite his availability after his departure from Real Madrid in the summer.
The match was also Spurs's biggest top-flight win at Old Trafford since a 4-1 victory in 1972. The only defensive arrival was young Diogo Dalot, who is a full-back, while he was joined by Fred and back-up goalkeeper Lee Grant.
However, former Liverpool defender and club legend Nicol has claimed that Spurs should not instantly be considered contenders for the league title this season and also added that they are not stronger than they were a year ago.
"From a strategic point of view, we didn't lose", Mourinho said of the performance.
One win and two defeats.
"Jose Mourinho has been the most successful manager along with Pep Guardiola in the last 20 years in football and he is going through a hard moment now over the last couple of seasons with Manchester United".
"I think the writing was on the wall as soon as the board did not give him the funds at the start of the year". "But we lost the game".
"Today I had the proof the best judge are the supporters", Mourinho said. During pre-season, the coach was critical of Anthony Martial, who didn't return to the United States quickly following the birth of his son, and Antonio Valencia.
"The first goal is always important in these games, just to get that breakthrough and then we really stepped it up another gear after that and it was great to see us finish 3-0".
"This is a good game for us to have". "It is about him giving the best that he has".
It ratchets up the pressure on the United boss and his team ahead of Sunday's trip to Burnley, where left-back Shaw knows a response is needed.
Jose Mourinho has cut a frustrated figure to say the least in recent months.
After Romelu Lukaku missed an open goal in the first half, Tottenham were clinical in a two minute spell at the start of the second half. Now, only the Belgian has managed to score as they lack effectiveness in the final third.