The 18-year-old was called upon early in the first half of Thursday evening's 1-1 draw with Dean Smith's side at Goodison Park to replace the injured Mason Holgate, who will now miss the remainder of the campaign.
The teenager, who had made his Premier League debut a few days earlier against Wolves, looked mature and confident in his spell on the pitch and has received a lot of plaudits for his performance.
Keane told evertonfc.com: “I thought he was brilliant but I wasn't surprised.
“He has shown in training since we came back he is a top, top young player. He had a bit of experience at Wolves, which will have helped him on Thursday.
“I am starting to feel old now, playing with Mason and Jarrad! I try to pass my experience to them, try to be a leader, try to be the loud one and help them get through it.
“I thought we [Keane and Branthwaite] defended well as a pair. He is a great lad, he works hard and he is humble.
“I am sure he has a great career ahead of him."