Gallagher, on-loan from Chelsea, scored the game's only goal when he drove through a crowded box early in the first half.
Bilic said: "He's got a bit of everything.
"He's very calm on the ball, he's very energetic, he loves to get in the box. A couple of days ago he twisted his ankle a little bit and there was a major doubt, but he wanted to play. He showed character and I'm really happy with his goal and his contribution. If he continues like this he could be massive for us."