Ibrox side Glasgow Rangers have managed to avoid defeat in Europe so far, while Celtic have struggled more.
Both Celtic and Rangers have made it through to the Europa League this season, and are battling in the group stages.
Rangers have actually made a brighter start than Celtic in Europe, and remain unbeaten in the competition.
But Rodgers admits that living up to expectations can be a tough ask for the Glasgow sides.
“Is the knockout stages of the Champions League a realistic target? You have to try,” he said.
“But of course, it’s getting more difficult and I’m a realist. At the same time, the expectations of Celtic and Rangers are to push on in Europe even though it’s extremely difficult.”
Gerrard has led Rangers to a series of impressive results in Europe this term.
Rangers have drawn in Spain with Villarreal, beaten Rapid Wien at Ibrox and drawn with Spartak Moscow.
Celtic, meanwhile, have found things more difficult. Rodgers’ side failed to make it through the Champions League qualification process, and they have only managed to pick up three points against Rosenborg in their Europa League group to date.
Celtic are next in action on Thursday against RB Leipzig, while Rangers take on Spartak.
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