McDowall skippered a Glasgow side that despite missing Sione Tuipulotu, Huw Jones, Scott Cummings, Rory Darge and the Fagerson brothers was able to grind out a 17-15 win over a Scarlets side that has impressed in this season's URC campaign.
Speaking to BBC Scotland, McDowall said: "It sounds weird, but it's probably one of my proudest nights in a Warriors jersey.
"A young team out there against a fully loaded team with internationals against us and we found a way to win, which is a nice thing.
"If you look back to that Bath [Challenge Cup] game a couple of years ago, we went down with a young team, Bayonne last year we went away - it's those types of games that define this squad.
"We talked about springboarding ourselves into Europe next week with a big win. Maybe it wasn't a big win, but it was a win and that's all that matters.
"Unbelievable effort from some guys, first time pulling on the jersey, some guys haven't played in two years, we battled and we got a win.":