The Ibrox side lost 4-2 on aggregate to Malmo in their third qualifying round tie despite the Swedish champions playing with 10 men in the second half at Ibrox on Tuesday night after the dismissal of midfielder Bonke Innocent.
Rangers had wiped out their 2-1 first leg deficit through a 19th minute strike from Alfredo Morelos but then lost two goals in rapid order early in the second half, mirroring the defensive lapses which cost them in Malmo seven days earlier.
"The most frustrating part is we've lost the second half to ten men,” lamented Gerrard. “Two throw-in situations we've not defended well enough. Besides that, I can't really at the moment think of too many things that went wrong.
"To be 1-0 up and then go 2-1 down, a bit of fear and panic set in. We've got the second half performance wrong and that's on all of us.
"We did really well tonight for 45 minutes. But we've got two restarts badly wrong and we've paid for it.
“The reality is at this level you can't concede two goals in the first leg and two in the second leg because you make things difficult for yourself.
“There is no way to dress that up. We need to be better in those situations. When you play teams at this level and you don't defend, then you will pay – and we have done.”
Having missed out on a potential bounty of around £30 million for Champions League group stage participation, Rangers now drop into the play-off round of the Europa League. They will face the winners of Thursday’s tie between Kairat Almaty of Kazakhstan and Alashkert of Armenia which is goalless after the first leg.
Rangers are next in action on Friday night against Dunfermline in the last 16 of the League Cup when Gerrard must try to arrest their current run of three consecutive defeats.
"We've lost three games out of four (so far this season) and at Rangers that's not good enough,” he said. “We now have to pick ourselves up and regroup.”