A 26-21 win over Sale was the perfect reaction to last weekend's shock 23-0 loss to Scarlets and sets Glasgow up nicely for next Saturday's clash with French giants Toulouse at Scotstoun.
Speaking to Premier Sports, Steyn said: "I'm really proud of the boys, especially our big boys up front.
"It's a really tough place to come and play down here and after last week the boys were really keen to bounce back."
Steyn said winning the aerial battle had been a focus in the build-up to the match. A brilliant take early in the second half set up the field position from which he eventually scored to put Glasgow in front for the first time in the match.
"You know how important it is now with the change of the laws," said Steyn, referencing the law change where teams now cannot block players chasing a kick.
"We knew how physical Sale's pack were and what a shift our big boys were going to put in so we knew that for us as backs, that's where we could get the pay and get them going forward."
Steyn said it was important to get points on the board early.
He said: "With the pool we've got, we've got Toulouse next week and Sarries and Clermont in January so there's no time to tip-toe around it. I'm massively proud of the way the boys showed up again today."
Toulouse open their campaign against The Sharks on Sunday and Steyn said having extra rest could be key for Glasgow after a tough encounter in Salford.
"The boys will be glad we've got an eight-day turnaround," said the skipper.
"We can refresh, get the bodies going and then what a spectacle to have at home at Scotstoun. The Glasgow fans will be buzzing to have a game like that.
"We know what a challenge they are, what a quality side they are. They've got threats all over the park. They'll go the 80 minutes, and we're just keen to try and go toe-to-toe.
"We've got to the point now where we kind of call Scotstoun the ice rink, you know, so we'll see if those big Toulouse forwards can come and do it at the ice rink."