The Portuguese was upset that the technology did not overturn a second-half penalty for the visitors when Eric Dier fouled Paul Pogba.
Bruno Fernandes equalised from the spot and then appeared to be fouled inside the box by Dier.
Referee Jonathan Moss pointed to the spot again, only this time VAR reversed the decision, leaving Mourinho frustrated with both moments.
“I’m not happy with the penalty or the second penalty,” Mourinho told Sky Sports. “I’m unhappy with the VAR, not the referee. In the game, he can make a mistake, give a cheap penalty. The VAR is there to do the job, I’m not unhappy with Moss, I’m unhappy with the VAR.
“I’m unhappy with Moss for the second penalty because he didn’t give the free-kick for [Serge] Aurier, then he gave a cheap, non-penalty, and VAR tells the truth.”
Mourinho was also full of praise for Eric Dier but emphasised how the option of five substitutions helped United more than the hosts as the game developed.
He added: “I think he [Dier] was fantastic, he played very well. I think Davinson [Sanchez] made one mistake in the first half, a technical mistake that gave [Marcus] Rashford a chance.
“Dier was absolutely perfect. It was not just Paul [Pogba], they had [Mason] Greenwood, [Odion] Ighalo, or Jesse [Lingard] – he can change the game. That’s what the five changes can do with a powerful bench with options.
“By starting [Erik] Lamela, [Steven] Bergwijn, Harry [Kane] and Son [Heung-min], they were really tired and on the bench we didn’t have that. In the next game Lucas [Moura] is back. Dele [Alli] is back I think. We have more options.”