Luck was in United's favour as they are also one step away from making it to the Champions League in the next season.
Chris Smalling let Harry Kane move in front of him for the second Tottenham goal after Wayne Rooney had lost Victor Wanyama at a corner for the opener.
United put in an underwhelming performance at White Hart Lane, but Mourinho was nonetheless pleased with what he saw.
The Red Devils are in the final of the Europa League against Ajax, and that was reflected in Mourinho's team selection for the game.
"If we want to try and get some results and protect players, which matches to protect players?"
"For my boys, it is a fantastic season - and I will prepare them for a wonderful final".
Manchester United go into the game aiming to finish their Premier League campaign on a high. It would be unbelievable.
We know that if we lose the final we won't play in the Champions League next season.
"I didn't see the red card incident but Eric was phenomenal". Some kept control in better ways than others.More news: Emmanuel Macron's first non-Europe trip focuses on fighting extremism
More news: Trump alleges 'witch hunt', denies trying to kill FBI probe
More news: Q4 2016 Sentiment Juniper Networks Inc (NYSE:JNPR)
Mourinho bristled at the question, responding: "I don't want to think about it in this moment - I want to think about the final I have to play".
"Ajax will be hard".
"I am not upset because we had to make that decision", he said about missing out on the top four.
"Tonight we suffered, but we're in the final and we've fought hard to get there".
So this week's match against Tottenham is another opportunity for Olosunde to make his Premier League debut. "But we are there and we go to the final".
United will come up against Dutch side Ajax at The Friends Arena in Stockholm on 24 May 2017 after they scraped through an even trickier aggregate victory over Lyon - winning 5-1 on aggregate.
MAROUANE FELLAINI was Jose Mourinho's unlikely hero last night as Manchester United battled their way into the Europa League final after a dramatic finish at Old Trafford.
United are sixth in the Premier League, 19 points behind Chelsea, with three matches left. But I don't feel like that. I don't know the way they think.