The Glasgow captain was at the heart of the quarter-final victory, scoring two tries, delivering a superb 50-22 and producing a crucial try-saving tackle.
Asked whether it was his best performance in a Warriors shirt, Steyn told the media: "I've got no idea. I haven't even taken the time to process that. I think I'm just happy. In recent weeks, I probably had moments as a captain where I was on the other side of it.
"I think of that Stormers game where I wasn't so good and had moments where I didn't show any of that. I'm just pretty happy to be out there at this time of year and hopefully be able to make a difference."
One of the defining moments of the match was Steyn's perfect 50-22, which helped Glasgow seize control at a key stage.
Reflecting on the kick, he said: "All the boys were screaming at me. We've got a call for the kick to that corner so Dan Lancaster and Staff [McDowall] were screaming for it. And I still second-guessed it.
"I was like, no, maybe I should just run it. But all the space was there. They'd shown us a bit in the first half, they were shutting the door on us pretty quickly. So it was pretty touch and go the whole way I was watching it. It was kind of like either side of the line and I just didn't want it to go dead. So I was probably more relieved than anything when it went out on the five.
"I don't really think too much about it. It might be a one-and-done and, you know. Gogs [George Horne] went down and said he couldn't pass and I had a couple of scrum half passes. So there was a mixed bag in there.
"We spoke before the game about all the memories we've had on the pitch this season and the boys who are leaving. It was more just about celebrating that and being able to enjoy that, being able to enjoy playing out there. We had a lot of fun out there."
Glasgow will now face the Bulls at Murrayfield, a venue familiar to many within a squad packed with Scotland internationals. The South Africans are also well-known opponents, having been beaten by the Warriors in the Champions Cup last-16 at Scotstoun earlier this season.
Steyn believes playing in Edinburgh can provide a boost.
"Yeah, definitely. Like Franco has said, we're playing in Scotland in front of our people. It does probably help us a little bit, just the familiarity of what it's like to field the box kick and how that kind of thing feels. The feel on the pitch, the width of it.
"But I think we'll more be buzzing about the fact that hopefully we'll be able to fill it with loads of Glaswegians, loads of Scottish rugby fans."