Marcus Rashford burst onto the scene last season with nine goals after Louis van Gaal handed the 19-year-old his senior debut in February.
But the six-capped England international has struggled for game time under Mourinho, starting just 10 Premier League matches this season.
The Manchester United academy graduate scored in last night's 2-1 FA Cup win over Blackburn to help the holders into the quarter-finals.
Jose Mourinho being careful with Manchester United youngster Marcus Rashford
Man United ace Marcus Rashford's new house
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Former Arsenal striker Smith believes Mourinho is just being careful with the youngster and is confident he'll get his chance to prove his worth.
"After he exploded onto the scene he was never going to continue like that," Smith told Sky Sports. "You have to take a dip as a youngster.
"And I think Jose Mourinho's just been very careful with him. He's had opportunities but he's not played as well as he would have wanted to.
Marcus Rashford burst onto the scene under Louis van Gaal
Marcus Rashford scored Manchester United's first goal in Blackburn win
"There's fierce competition for places up top. Wayne Rooney can't even get in so it's no disgrace for a lad of Rashford's age.
"But he's clearly a lad with great talent and you want to – I think they have done – tie him down for a few years to come.
"That goal [against Blackburn] will do him a lot of good."