The Red Devils brought in the Portuguese full-back in a £17m deal from 2004 Champions League winners Porto in the 2018 summer transfer window.
Manchester United manager Jose Mourinho started Dalot at right-back in the absence of Antonio Valencia for the Champions League opener at Young Boys.
Goals from Paul Pogba and Anthony Martial secured three points for the Red Devils as Dalot helped the visitors to keep a clean sheet in Switzerland.
Dalot has only made one appearance for the 20-time English champions so far, but the summer signing will be hoping to retain his place for the visit of Wolverhampton Wanderers on Saturday.
Former Manchester United midfielder Hargreaves was impressed with Dalot’s debut in Europe on Wednesday night.
“He’s a terrific crosser of the ball and technically he’s very good,” Hargreaves told BT Sport. “For 19, he looks really good.”
Manchester United are in eighth position in the Premier League table following a mixed start to the season.
The Red Devils lost to Brighton and Hove Albion and Tottenham Hotspur in the English top flight.
The 20-time English champions were 2-1 winners against Watford in their last Premier League game before the return of the Champions League.
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