The Warriors ran out 20-7 winners over a battling Scarlets team in their first match at Scotstoun since February.
Speaking to glasgowwarriors.org, Wilson said: "I think we managed that game extremely well for the first hour. We were dominant in almost every aspect of the game, and we probably should have gone on and done more with our ball and opportunities to be honest.
"Our discipline let us down a little bit late on when we let them come back into the game a bit, but the important part was getting that first win of the season.
"Don't forget, that was a quality Scarlets outfit with Welsh internationals and British and Irish Lions that we've just beaten."
"We had a game plan that we stuck to, and we applied pressure well," said Wilson.
"They're a really good side and you have to stay in the battle with them.
"Although we let them back in, we still held them to just the seven points, which was really pleasing for us. I thought our set-piece was excellent and that gave us the platform."
The PRO14 now takes a week off to allow the Heineken Champions Cup and European Challenge Cup to reach their respective conclusions, before Wilson and his side return to action against the Ospreys in two weekends' time. Whilst Wilson admits that room for improvement still remains, the result is the only thing that matters for the Glasgow boss.
"Our work at the breakdown and collisions was a lot better than theirs I thought, and our discipline was much improved from last week for the first hour or so," he said.
"We let our foot off the gas a bit and we'll look at that, but tonight was all about the win."