Mourinho guided Porto to an aggregate win over United five years ago when a 1-1 draw at Old Trafford took them through to the quarter-finals and ultimate success in the competition.
A repeat on Wednesday would suffice for Inter to progress to the last-eight for the first time since 2006 following a 0-0 draw in the first leg in Italy.
"That goal (by Costinha) gave us the chance to win the Champions League and our careers were never the same again. That goal opened doors for me in England," Mourinho, recalling Costinha's late equaliser, told reporters on Tuesday.
"But that's over. I am not one to look back and be happy with what we've done. I want more and tomorrow and we will try and do it against a very good team. We know what we need to do and we know how we can create problems for them.
"We are prepared for the game and I believe we can do it."
Mourinho left Porto to enjoy great success in England with Chelsea and in five visits to Old Trafford he has lost only once, contributing to an overall record of just one defeat in 13 matches against United manager Alex Ferguson.
"The first time I came to Old Trafford everything was new for me," Mourinho added.
"Now it looks like home because for four years I have come here a lot, not just in the Premier League but also in the semi-finals of League and FA Cups.
"It has become part of my life. It's a different feeling. I even know the groundsman."
Mourinho said that he has encountered a different football culture in Italy since taking over at the San Siro in June last year but hopes to implant some of his natural confidence into his players as Inter look to knock out the Champions League holders.
He added: "Our Italian friends see football in a different way. They see football like a bit more of a drama in difficult moments.
"I was never like this and since working in England I have even improved myself in that aspect. Football is never a drama. Football is always passion and pleasure.
"It's a pleasure to play tomorrow and that's the feeling I want to give to my players. They have spoken for the three weeks about the drama of Inter always going out in the last 16.
"I prefer to think in a different way and the possibility of Inter knocking out the world champions. It's a different way of looking at the picture."
United dominated the first leg without being able to score and Mourinho believes the winners on Wednesday will be the team that holds their nerve.
"It's a goal, a detail, a mistake. It's a game for people that can handle the pressure because it's game of high pressure for both sides."
