It follows recent debates over United's penalty count with Liverpool boss Jurgen Klopp suggesting Ole Gunnar Solskjaer's side had won more than his over a far shorter period.
The England striker, 23, said Mourinho changed his attitude in the box.
He added: "Jose said, 'if you're not savvy about the way you do it, then you are not going to get given it'."
Mourinho left United in 2018 after two years in charge, and since Solskjaer's first league match in December of that year, the side have been awarded the most Premier League penalties (27).
Last season United broke the record for the most spot-kicks awarded in a single Premier League season (14) and this campaign they have won 11 in all competitions.
"When you are making runs in behind or you are dribbling with the ball and you see a challenge coming, you don't want to get tackled because you are looking at an opportunity to score a goal," said Rashford, who won the Football Writers' Association 2021 Tribute Award on Thursday.
"But there have been times when we have probably not got penalties.
"When Jose was manager, there were five or six times I can remember where I should have had a penalty."
Upon being given the advice, Rashford said: "It was something in terms of development you have to learn and understand."
The forward has won 11 penalties for United at domestic league and European level, although eight of those have come under the management of Solskjaer.