Having delivered a perfect pool stage - including a memorable comeback win over Stade Toulousain - and battled past Bulls in the last 16, Franco Smith's men welcomed RC Toulon to Scotstoun knowing a place in a home semi-final awaited.
However, with key absentees including scrum-halves George Horne and Jamie Dobie, alongside a depleted second row, the Warriors were unable to impose their usual attacking rhythm. Toulon's physical edge and clinical execution ultimately secured their progression to a semi-final clash with Leinster Rugby in Dublin.
"Everyone's gutted," said Steyn. It's difficult not to reflect on what's been put into this jersey this season and what that's meant to everybody and how much hard work has gone in from players and coaches.
"We desperately wanted more for this campaign, and it's not to be. I think that's credit to Toulon because they've got that championship DNA and I think they showed it more consistently than we did."
Despite the setback, attention now turns quickly back to the URC, where Glasgow remain in a strong position at the top of the standings.
"We've been in this position before where this tournament's ended for us and there's lots of guys that have learned a good lesson. We've got a core of this group that's been on this journey since Franco's been here that understand what you need this time of year and now all the energy will be going into making sure we try our best to not let another chance slip by in the URC."
There is little time to dwell, with a demanding South African tour looming. Fixtures against the Lions in Johannesburg and the Stormers in Cape Town will provide a stern test as the Warriors push to secure a top-two finish.
"I think if today showed you anything, the way the pool stage has gone and then the knockout today, you just don't look further than the week ahead," Steyn said.
"We've got the South Africa trip and then we come back to Cardiff (at home) and Ulster (away, in their final league game) and that's what the message is going to be. It's about putting everything into every week now and every training day, because we don't want to feel like this again.
"We've got a good enough group that's been through enough. We've lost to Toulon in knockout games before [a European Challenge Cup final in 2023] and we've learned lessons. As leaders, we'll sit and look at how we try to adapt to that on the field and get ourselves back on track.
"There's no point dwelling now on what the occasion did to us. It's about making sure that we're ready for next week first and foremost. Lions away is probably one of the toughest away games in the league, so we'll take those learnings and turn them into energy for that game.
"It's a really difficult tour. They're difficult places to go and play, and that's exactly what we need in the build-up for the (URC) knockout stages. It's something we've learned under Franco that you take everything head-on. We're looking forward to the challenge."
Injury concerns remain a factor heading into the tour, with Franco Smith confirming lock Max Williamson faces four to six weeks on the sidelines. With Alex Craig already ruled out long-term and both Scott Cummings and Gregor Brown unavailable, resources in the engine room are stretched.
Further absences include Rory Darge, while Adam Hastings remains a doubt following a late injury against Toulon. Young fly-half Matthew Urwin could therefore be called upon to support Dan Lancaster, while Sione Tuipulotu also appeared to have picked up a knock.