Spurs were on course for three valuable points in the race for a Champions League qualification slot when David De Gea failed to keep out Steven Bergwijn's first-half strike.
It could have been worse for Tottenham, but another United penalty in stoppage time was rescinded by VAR after Fernandes went down under apparently no contact from Dier.
"I am not happy with the penalty and not happy with the second penalty," Mourinho said. "I am unhappy with the VAR, not the referee on the first, the referee can make a mistake but VAR is there to do the job.
"In the second I am unhappy with [referee] Jon Moss because he did not give the free kick leading up to it and then gave another penalty. In this case the VAR gave the truth.
"We knew that we could have a penalty against because we know they have an incredible record of penalties given."
Mourinho also said VAR should have been used to book Fernandes for simulation after appearing to fall theatrically before the second penalty was called.
While the Portuguese coach was left frustrated against the club that sacked him last season, United manager Ole Gunnar Solskjaer praised Pogba who came off the bench in the second half for only his ninth appearance of the season.
The France midfielder has been sidelined by ankle injuries and had not appeared since January, but sparked United into life when he replaced Fred just past the hour mark.
"Paul did everything a midfielder should do, he tackled, won passes and showed some skills so fantastic to have him back," Solskjaer told reporters.
"He's had a frustrating season with his injuries. Paul has shown today how he can contribute and I just look forward to getting him fitter and seeing Paul getting back to his best."
Solskjaer paid tribute to United's fitness staff as his side ended the match strongly. Mourinho, however, said his players had grown tired towards the end of a fast-paced game.
"I liked my team performance for 70 minutes, I felt we were in control and I felt we gave them the kind of game that they don't like very much," Mourinho said.