The big South Afican was a key figure in last season's URC triumph, and he's become a firm favourite with the Glasgow support, which makes it all the more disappointing that he'll be leaving Scotstoun at the end of the current campaign to join French side Brive.
Venter produced a player of the match display against Leicester and went over for two tries to help his side into the Champions Cup quarter-finals.
Warriors now head to Dublin to face Leinster, who thumped Harlequins 62-0 to book their spot in the last eight.
Leinster are one of the tournament big guns and will be overwhelming favourites to reach the semi-finals, but Venter says Glasgow are chasing their own Champions Cup ambitions.
"We're here to win the thing," Venter told BBC Scotland.
"I think Leinster's performance against Harlequins was next level and all kudos to them. We'll meet them next week and we'll definitely take the confidence [from beating Leicester] and be up for it.
"I'm also gutted [to be leaving]. I love this place, I love the Scots, I love Glasgow. It's just a privilege to wear this shirt every day.
"It's two cups to win for me and just to give everything for this club that's given so much to me."