Louis van Gaal`s men now face their toughest tests of the season so far with games against Premier League leaders Chelsea and defending Champions Manchester City next in line.
The Reds are now 10 points behind Mourinho's side but Van Gaal says it is possible to close in on Chelsea.
"Ten points is a lot. It's possible to do it, but it will be difficult. If I say we can do it then I am arrogant, but I have done it a lot of times before." the Dutchman said.
"Chelsea and City are another level, with no disrespect to West Brom. Are we far away? We have to see if we can beat them and after those matches I can tell you 'yes' or 'no'."
Louis van Gaal admitted he is delighted with the style his team is adopting despite needing a dying-minute goal from Daley Blind to secure a draw at West Brom. He added: "We dominated the second half and that's what I want. I want that, but I don't want 2-2.
"I'm happy with the style, but not the result because I see it as two points lost. I believe we should have eight points more but that's a matter of time before we stop the errors."
The United boss also insisted that the style of play he is implementing won't be changed in favour of shoring up the defence.
He said: "I believe in this way. Football is made to be played in an attractive way.
"You could say we have come from behind twice but I felt we gave away two goals and were the better team."