Connor McLennan added to an early goal from Niall McGinn to see the Dons through to a last-four meeting with holders Celtic.
And Gerrard, who had been targeting the Scottish Cup after all but conceding the Scottish Premiership title to the Parkhead side, spoke candidly after the Tuesday night defeat.
Branding the performance “disappointing”, Gerrard told Rangers TV: “It’s a huge blow, this was a huge game for the club - for me, the players, all the fans - and we’ve let the supporters down.
“I take full responsibility for it; we were nowhere near good enough. I thought the best team won, we started the game extremely poorly, and we never really got much better from there.
“We gifted them a goal and I think everyone knows if you let Aberdeen get their noses in front they’re a tough nut to crack and that was the case.”
A mistake from Glen Kamara gifted the Pittodrie side the opener after just three minutes, McGinn capitalising on the wayward pass to slot the ball past Allan McGregor.
Asked if the early goal had forced him into changing his tactics, Gerrard said: “No, because you’ve still got belief and confidence that the players can react in the right way and try and get back in the game.
“But the reality is we didn’t test their ‘keeper nearly enough over the 90 minutes. We’ve got no complaints in terms of the result - they deserved it, they wanted it more in certain areas of the pitch, which is a major concern.”
The Ibrox boss admitted he hadn’t spoken to the players, adding: “It’s extremely frustrating right now. I don’t feel ready to speak to the players just yet, because I’m angry.
“[In the] short term we have to regroup, and push on and try and finish the season as strongly as we can.
“I don’t think anything I say can make [the fans] feel better short-term; but what I will say is we’ll be back. In terms of cup competitions, we’ll be back, we’ll be better and we’ll give it a better go when the time’s right.
“All we need to do is finish the season as strongly as we can and that starts [on] Saturday.”