A late goal from Anthony Martial proved the differences between the two sides and kept United second in the table, five points behind Manchester City and three clear of Spurs. At full-time, the Portuguese put his finger to his lips while looking towards a TV camera, before then shaking hands with Tottenham manager Mauricio Pochettino.
When quizzed about the gesture, the United manager said: "Some people speak too much.
"Calm down, relax a little bit. Don't speak too much, speak, speak, speak, relax."
Asked whether his rebuttal was aimed his critics, whom he labelled "Einsteins" last season, the Portuguese replied: "Yeah, relax a little bit. Don't be so nervous, don't be so excited. Calm down a little bit. The opposition bench did their job, super-correct.
"It has yet to arrive, the match where myself, Mauricio [Pochettino], my staff and his staff, have a problem."
Mourinho had been under pressure over the last two weeks, as United's overly cautious approach saw them earn a 0-0 draw at Anfield against Liverpool, before they suffered their Premier League defeat of the season away at Huddersfield a week ago.
Following the latter result, Mourinho had openly criticised his players' attitude but was rewarded with an improved performance against Spurs, which saw United edge a largely cagey game where chances were at a premium.
"If the result is 0-0 or 1-1 my feelings with the players would be the same because they gave absolutely everything, every ball was like the most important ball of their career," said the United manager.
"The concentration and focus was there and we cannot forget the quality of the team we were playing against."
United started the game on the front foot but their verve soon petered out as Spurs grew into the game and there was nothing between the two sides at halftime. The host went twice closed to opening the scoring early in the second half, before Dele Alli squandered the best chance of the game to put his side in the lead with just over 20 minutes to go.
The England midfielder's miss was to prove costly as the north Londoners conceded 10 minutes later, as Martial pounced on Romelu Lukaku's flick to fire past Hugo Lloris to clinch United's third 1-0 win against Spurs at Old Trafford in the last three seasons.
"Both sides were trying to win, and that's what I like to see," said Mourinho, whose decision to replace Marcus Rashford with Martial was met by a few boos.
"Maybe we got a bit lucky in the end, they had a good chance just before we scored, but in the whole match I think we produced more chances to win than they did."
Saturday's 1-0 win means United have gone over a year unbeaten at Old Trafford, where they have won all their Premier League games this season without conceding a goal.