Anthony Martial's late strike stole the points for United in Saturday's early kick-off, getting them back to winning ways in the Premier League after poor performances in a draw at Liverpool and last week's loss at the John Smith's Stadium.
If United fans wanted a more expansive performance they did not get it, but Mourinho's three-man back line of Eric Bailly, Phil Jones and Chris Smalling held firm against a Spurs attack shorn of Harry Kane.
Having cemented their grip on second place, moving three points ahead of Mauricio Pochettino's side, Mourinho hailed the response of his players.
"We all feel we have to win every match so that's why I felt disappointed at Huddersfield," Mourinho told Sky Sports.
"In that match, it looks like we didn't know the responsibility, we didn't know the ambition. Every point is a precious point.
"Today, if we drew the match or if in the last minute we concede I would never be against the players because from minute one, every ball was like the last ball of their careers, they gave everything and I'm really happy."
He added: "Both teams were trying to win but both knowing the opponent was strong.
"But I think the only team that had opportunities I think was us, I think just the Dele Alli chance, apart from that we controlled them very well and I think we had more chances to win the match.
"[It was a] big football match, tactically difficult for both teams, tactically difficult for players, a big match.
"We kept trying by bringing fresh people but for the same positions, the same dynamic as we were telling you. We were both trying to win but both knew one defensive mistake and we could win the match which happens to them.
"But I think we were pushing a little bit more after 15-20 minutes the balance came to the match and in the second half we created more problems with more movement.
"With [Marcus] Rashford tiring, Martial comes better running with the ball. We tried and I think we deserved the victory."