Rashford has been given the huge task of leading the line for Manchester United in Zlatan Ibrahimovic’s absence as the Swede completes a three-game ban for violent conduct.
The young striker hasn’t scored in the two games since but has shown desire and commitment which Murphy believes has opponents scared.
“He’s got confidence and maturity that you wouldn’t expect from a young lad, especially one playing for a club like Man United,” Murphy said on BBC’s Match of the Day.
“He’s always in there and defenders are terrified of him whenever he’s got the ball because they know he can run past him with or without the ball.
“He’s got a big future, he just needs more minutes.”
Rashford hit the headlines last season when he scored two goals in both his Europa League and Premier League debuts against FC Midtjylland and Arsenal.
His form led him to be called up to England’s Euro 2016 squad where he came off the bench against both Wales and Iceland, but his career has faltered slightly under Jose Mourinho.
Played primarily on the wing to accommodate the arrival of Ibrahimovic, Rashford has contributed to just four Premier League goals so far this season (three goals, one assist).
Rashford: the Premier League’s most experienced teenager
Rashford has enjoyed 1,165 minutes of top-flight playing time this season so far. The only La Liga teenager who can boast more is Alaves’ 19-year-old left-back Theo Hernandez.
Ousmane Dembele (1,384), Borussia Dortmund’s 19-year-old attacking midfielder, is the only Bundesliga talent aged under 20 to play more minutes than Man Utd’s young striker.
Meanwhile, Serie A is enjoying a wealth of up-and-coming talents. Leading the way, of course, is AC Milan’s goalkeeper prodigy Gianluigi Donnarumma, with a mammoth 2,610 minutes of top-flight action played. The 18-year-old goalkeeper is followed by Assane Diousse of Empoli (1,862), Manuel Locatelli of Milan (1,427), Fiorentina forward Federico Chiesa (1,174).
It is Ligue 1 that currently offers the most minutes to teenage players. Those to have played more than Rashford include Toulouse goalkeeper Alban Lafont (2,610), Malang Sarr of Nice’s back line (1,936), Nantes midfielder Amine Harit (1,871), Marsaille attacking midfielder Maxime Lopez (1,580), Metz’s Ismaila Sarr (1,536) and Cane forward Yann Karamoh (1,404).