Rashford was deadly at Old Trafford, grabbing both his goals within the first twenty minutes of action to set United up for smooth sailing for the rest of the match.
This season, the England worldwide has now scored six times in the league, but he has mostly been used as a substitute.
"'If he has one or two not good games, he puts him out", he added.
Saturday's victory was the Portuguese manager's 68th Premier League game as United boss and Rashford has played a part in 59 of them.
"'It's a pity that his manager is Mourinho because you want to give him time and he can make mistakes".
The 20-year-old striker has scored 12 goals in 40 appearances for the Red Devils this term but De Boer claimed he should be starting more matches under Mourinho.
José Mourinho has given a withering critique of Frank de Boer, describing the former Crystal Palace manager as "the worst manager in the history of the Premier League".
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"If he was coached by Frank he would be coached how to lose because he lost every game".
"He was saying it is not good for Marcus Rashford to have to be coached by me".
De Boer was appointed Palace manager last summer on a three-year deal but was sacked just four games into the season and replaced by Roy Hodgson.
The midfielder - who surprisingly started the goalless first leg on the bench in Spain - was injured on the eve of the Liverpool clash and was conspicuous by his absence from the section of training open to the media on Monday. I try to give the best to the kids, education.
Mourinho was in spiky mood ahead of the visit of Sevilla, repeatedly making self-deprecating remarks about his Champions League triumphs as Porto and Inter Milan manager.
Mourinho went on to credit United's academy staff and his predecessor Louis van Gaal for their role in Rashford's development and insisted the player remains in safe hands under his own leadership.
'But if you go to his numbers and how many matches he played with me last season and this, I would say probably he's in the top five players with more matches in the two seasons.