The Scottish side were eliminated from Europe after a 1-0 defeat to Bayer Leverkusen on Thursday (06.08.20) but Gerrard has taken pride in his team's European adventure, which began last summer back in the qualifying rounds.
Speaking to RangersTV: "We look back with immense pride, we have done ever so well. I think we have done the fans proud if you look at the whole journey."
Rangers bowed out after a 4-1 aggregate loss to the German side and Gerrard has urged his team to strive for better when they return to continental competition.
He said: "There is no point looking back, we need to really respect this level and individually and collectively keep trying to strive for better.
"Of course we will keep trying to add bodies into it to make us better, but every single day on the training pitch we need to keep trying to improve on the things that didn't go well."
The 40-year-old coach also addressed the future of striker Alfredo Morelos, who has been linked with a move away from the Ibrox side.
Gerrard told BT Sport: "Everyone knows he's had his head turned.
"If a bid comes that the board like, and if the player tells me face-to-face he wants to go, we'll see what happens.
"My focus is on the team and the players that want to be here."