Gilmour, 20, made his first international start in the Group D clash at Wembley and put in a man-of-the-match performance as Scotland deservedly took a point from their hosts.
Robertson said Gilmour can have a great career but he is already a special talent.
"I spoke to him in the hotel today and I just looked at him, to be fair to Billy nothing fazes him and that is why I believe he can have as many Scotland caps as he wants," the Liverpool defender said on ITV.
"He has got a huge future ahead of him, but the here and now is pretty good as well."
Scotland were worthy of their draw at Wembley and had the better chances as Che Adams missed two good opportunities, Lyndon Dykes had an effort cleared off the line and Jordan Pickford saved well from Stephen O'Donnell.
Robertson said his side deserved to win but have to use this performance to get the win against Croatia that would send them through to the knockout stages.
"I think we did enough to win, I don't think many people can argue with that," he added.
"We had the big chances, at times we kept the ball superbly well and frustrated them and on another night we could have come away with more.
"We will take a point, it keeps us alive, but it's important we use this feeling going into Tuesday and it's important we try and use it to get a positive result which we need to get through the group.
"Credit to the boys in there, a really good result but it is important it is not a pointless result. It is important that we use it to try and get out of this group."