Mourinho, speaking at a news conference at White Hart Lane before Real protect their 4-0 first leg advantage on Wednesday, said his team were coming to "finish the job" and would be looking to win rather than defend their comfortable lead.
No team has ever overturned a 4-0 first leg deficit to advance in any European competition and Mourinho is not about to let his side become the first to suffer such an unlikely fate.
"We have to respect Tottenham and we have to respect football," Mourinho told a packed suite at the stadium, "because football sometimes can betray you and we cannot give them the chance of doing that.
"That's why we are coming here to play seriously, especially for me and people like Xabi (Alonso) who know the mentality of English stadiums and English supporters, English teams. They will try everything.
"Harry Redknapp (Tottenham's manager) is a good friend of mine and if I put myself in Harry's position, imagine we had lost 4-0 here and we go to Madrid for the second leg, I wouldn't throw in the towel. I would do everything with my players to try and get a miracle.
"The only thing I say is we have to respect our opponents.
"We have to play seriously, but at the same time I don't think five goals will be enough for Tottenham to beat us, because I think we are coming here to score goals."
Real are bidding to lift the European Cup for a record-extending 10th time but Mourinho refused to talk about the likely prospect of facing Barcelona in the semi-final, and instead concentrated on Wednesday's game.
"Playing Barcelona means nothing to me now, it is all about tomorrow's game and I will pick my best side for the match.
"I think that some of the players find themselves in a slightly complicated, tough situation - a delicate situation.
"The players need to be intelligent, they need to be bright, they need to be aware. They know what their own situation is.
"I think we have to respect the opponent, we know there is quite a difference in the scoreline, but we still have a job to finish tomorrow night."
Thank you for reading 5 articles this month* Join now for unlimited access
Enjoy your first month for just £1 / $1 / €1
*Read 5 free articles per month without a subscription
Join now for unlimited access
Try first month for just £1 / $1 / €1