The Belgian striker has scored three goals in as many games since making the move to Merseyside, including two in the 3-2 home win over Newcastle on Monday.
Fernando Torres has been the only Chelsea forward to find the target in that time, with Mourinho criticised in some quarters for allowing Lukaku to leave.
But the 20-year-old has offered his support to Mourinho, emphasising the fact he was the driving force behind the move.
"I did not know if I would be playing for Chelsea so I asked the manager to let me leave. We spoke and I told him," Lukaku told the Daily Telegraph.
"It's unfair to criticise Mourinho for letting me go because it was my decision.
"He knows what he is doing. He has won so many titles and I have too much respect for him to wish anything but the best.
"But there comes a point where you must think about yourself to show everyone that you can shine and be one of the best strikers in the league.
"I could have stayed and fought, but it was not about the competition. When you are a 20-year-old you need minutes. I lost my place in the national team because I did not play for a year with Chelsea.
"I want that position back. I want to be in a top team and play. You only get better if you play so the best thing was to leave.
"He'd called me into his office 10 days before the end of the window. I did not want to tell him what I wanted to do at that point, but he was very open and direct.
"I always wanted to work under him and even the time in pre-season he taught me lots I'm grateful for but I had to make a choice."