Reaching the Europa League group stages for a third year running is "fantastic" - but Steven Gerrard says his team will be judged on "success in May".
The Ibrox club beat Galatasaray 2-1 in the play-off round, thanks to goals from Scott Arfield and James Tavernier.
But Gerrard says his side must deliver at the end of the season - with Celtic aiming for a 10th consecutive title and a cup at stake - to meet expectations.
"This club is built on success and success is trophies," he said.
"They're difficult shoes to fill because of the fantastic teams in the past that have been successful and the expectation doesn't change. But we're aware of that and we deal with it.
"If we keep performing like we did tonight, if we keep moving this group of players forward, and adding the right players to it, maybe we can."
Thursday's result was an 11th consecutive game in all competitions without defeat for Rangers and ensures they claim a place in Pot 3 of Friday's group stage draw at 12:00 BST.
Gerrard says his side deserve credit for securing qualification in difficult circumstances.
"This run was more difficult because we haven't got the crowd," he said. "We haven't got the passion, the roar, and the support from the terraces and you only get one game.
"Tonight, to a man the players were outstanding. We gave them a gameplan but they have to go out and carry it out, the players deserve all the credit."
The Rangers manager also reserved special credit for captain Tavernier, whose goal turned out to be the winner.
"His consistency has been outrageous really," he said. "I know on the outside people make noise about James but the important thing is he's loved on the inside and we appreciate what he does.
"If he was the perfect full-back he probably wouldn't be here, but he puts himself out there and his numbers for a full-back - no matter what league or level you play at - are outstanding."
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