Chelsea Defender Kurt Zouma has hailed Gilmour's performance on Tuesday saying the young scot played with great maturity and confidence.
"Unbelievable performance, very mature in his game, and calm and clever as well, with the ball and without the ball," said the French centre-back.
"He was fantastic, like he is training. He is training very good. He is very confident and he can keep the ball, he is running around and pressing the guys.
"He has a bright future ahead of him, he just needs to keep working hard."
Zouma also wants his teammates to keep the same level of focus and concentration in their next game against Everton.
"Everybody was fighting a lot for every ball, everyone running around and defending and attacking. It was a good game to watch I think and we did a very good game," he added.
"Any clean sheet is good but especially against Liverpool. We know they have great players up front, they have a great team, and we did very well defensively and it is not just about defenders, all of us as a team played very well defensively, and offensively. We could have scored more.
"We did a good game but we need to stay focused because there are games when we can play good, and others when we are so-so. Maybe players are a bit tired, I don’t know, maybe we are not focused enough.
"Against Liverpool, this is the mentality we need to keep every game. We have a very important game on Sunday [against Everton], we need to get the win at home and move on from there."