Warriors ran in five tries to seal a 36-18 victory over the South African side and set up a semi-final showdown with Leinster in Dublin next weekend.
Henco Venter, Jack Mann and Tom Jordan are among a number of players leaving the club this summer, and Steyn was delighted they were able to enjoy a special night under the lights at Scotstoun.
"If it is the last one at home then I'm really chuffed for those men because they deserve a send-off like that," Steyn told BBC Scotland.
"It was just an unreal night, the way the fans got behind us. I got goose bumps the way they clapped Henco off at the end.
"We're really chuffed that we've earned another week to be out there with them and ready to rip into it.
"At this time of year it's not about being perfect. It's about being able to kind of roll with the dice and just keep going no matter what.
"I was really proud of our big boys up front. I thought the way they defended when we were close on our line really set the tone for us and then the backs were good off the back of that."