Rashford reacted angrily to a challenge from Phil Bardsley with just under 20 minutes remaining at Turf Moor, butting heads with the former United defender and subsequently being given his marching orders.
The incident did not affect the result as United ran out comfortable 2-0 winners, but Mourinho was unhappy with his striker, who had only been introduced as a sub 10 minutes earlier.
"I don't know what happened. I would say it was naive. It was a kid and a very experienced man. Bardsley's been in the game for 20 years and Marcus is a naive boy," Mourinho told BBC Sport.
The victory saw United return to winning ways after back-to-back defeats at the hands of Brighton & Hove Albion and Tottenham Hotspur.