A header from Harry Kane and a Lucas Moura double condemned United to their second successive defeat in the Premier League, leaving the North-West giants sitting in 13th place in the top-flight standings.
Mourinho came in for criticism before and after the match, but Allardyce has said that the Portuguese cannot be blamed for the latest setback, with United having created 14 more shots on goal than the visitors.
Allardyce told talkSPORT: "United had 57% possession, 23 shots at goal and five on target. Tottenham had 43% possession, nine shots on goals and five on target. It's only about Tottenham's finishing that got them the victory – normally that result would never happen.
"So is it a freak result? When you've had 23 shots at your own place and you have not scored, that is not the manager's fault, but the manager always gets blamed at the end of the day.
"Mourinho has set his team up to attack, they've created enough chances and opportunities to win the game comfortably, they failed to take those chances and they ended up being sucker punched by some pretty poor defending."
United are next in action when they make the short trip to Turf Moor to face Burnley on Sunday.