For last night's defeat to Manchester City, Drinkwater finally made his Premier League debut for the Clarets four months after joining from Chelsea and three months after suffering an ankle injury in an incident outside a Manchester nightclub.
Pieters said: "I'm really happy for him.
"He's waited for a long time to be in the team and I'm happy for him to get his first performance in. He would have been happier if we got a result I'm sure, but at least he got his first minutes in with us. Hopefully he can continue.
"It takes time but that's normal, he didn't play for a while, but he's looking good, he's feeling well. He's a great guy, he's funny, he fits perfectly.
"Everyone can see he's great on the ball, good passing, strong on the ball as well. And he brings calm in the team so hopefully he can get a couple more games to show it to us and show it to everyone."
Drinkwater's loan ends on January 6, with no indication as yet that Burnley might look to extend it.