Tarkowski has impressed for the Clarets in the Premier League this season, and the 25-year-old was rewarded with a start against the Azzurri at Wembley Stadium.
The centre-back conceded a controversial penalty as the two nations played out a 1-1 draw, but Dyche was impressed with how the international rookie performed on his first taste of action away from domestic football.
At a press conference, the 46-year-old told reporters: "I was really pleased. I don't think it's easy anyway to play for England. I don't think it's easy to play for England on your debut at home.
"I don't think it's easy to play in a back three and I don't think it's easy to play on the left of a three. When you add all of that in, with the new group, I thought he did very good.
"Nice and calm, played steady, organised when he needed to be. He did the basics very well and just kept his simplicity."
Tarkowski has made a total of 25 appearances for Burnley in all competitions this season.