Leeds United Under-21s lost to their Liverpool counterparts on Tuesday evening.
Coyle started the Premier League Cup last-16 tie at Tranmere Rovers’ Prenton Park and played for the entire 90 minutes.
The 20-year-old defender failed to guide the West Yorkshire outfit to victory, though, as Liverpool edged the encounter 1-0.
Daniel Trickett-Smith’s goal on the stroke of half time proved to be the difference between the two sides.
Hart was impressed with the performance of right-back Coyle, who recently made his debut for the Leeds first team.
“I look at people’s attitude when they come back,” Hart told Leeds’s official Twitter page about Coyle. “He is a terrific lad, terrific attitude, no different, and I thought his performance was excellent.”
"(Jordan) Botaka and (Lee) Erwin worked really hard," added the 62-year-old.
On the overall performance of the team, Hart said: "I thought we played very well, especially in the second half. I thought we gifted them the goal, but I was extremely pleased with some really good performances."
Meanwhile, Leeds’ first team are in action on Saturday afternoon when they take on Bristol City at Elland Road in the Championship.
Steve Evans’s side are 17th in the league table at the moment with 32 points from 27 matches, just eight points above the relegation zone.