Martin O'Neill described Celtic's defeat to Rangers as a "wake-up call," admitting his side were "second best" at Ibrox.
Goals from Dan Neil and Kevin Kelsy secured Rangers' place in the Premier Sports Cup semi-finals against Aberdeen, leaving Celtic with just one shot on target throughout the match.
O'Neill said: "We were well beaten in the end.
"I thought the first half we didn't capitalise, we had a couple of really decent chances when we'd broken their press.
"But on the day, just second best."
He stressed the importance of the fixture, stating that there needs to be a realisation of "how big" the game is.
"It's so important to the fans, so important to everybody.
"It's still one of the great fixtures in European football, if not the world.
"And people have got to know that. That's the point.
"We'll have to try and learn from it."
He hopes the loss, Celtic's first domestic defeat since March and only their second in all competitions this season, serves as a wake-up call.
"We play next Sunday, we've got a midweek game. I think, hopefully, it's a wake-up call.
"I have to look at myself for a start, then I look at the team.
"We were second best."
Though he wasn't surprised by Rangers' aggressive approach, fO'Neill was taken aback by his side's lack of attacking threat.
"I think you have to be able to deal with it.
"You deal with any sort of permutation that the opposition put in front of you.
"That's their prerogative, to do exactly that."
He attributed the defeat not to systems but to misplaced passes and poor decision-making when in possession.
"I think, we did misplace a lot of passes today when we were comfortable and choosing the wrong option when we were on the counter-attack."
O'Neill was particularly surprised by the lack of opportunities created.
"The one thing that I felt, and I think I've been saying to you for weeks, certainly domestically, we look as if we can create.
"So it didn't materialise today. So we have to try and find out the reasons why."
Attention was drawn to his decision to start on-loan Wolverhampton Wanderers goalkeeper Sam Johnstone ahead of Viljami Sinisalo.
ohnstone made his debut against St Johnstone in midweek and kept a clean sheet, but failed to convince at Ibrox, ceding possession inside his own area after four minutes.
O'Neill defended his decision, saying: "I want people to experience these games, because what other way am I going to learn about what people can or cannot do?"
He did, however, single out 19-year-old Colby Donovan for praise.
"Me personally, I think young Colby has come out of this with great credit.
"I think he's an absolute warrior.
"Sometimes we misplace passes, but he's got a big heart.
"I think we can all learn from that."
With no Celtic supporters allowed at Ibrox, the team faced a wall of noise from the Rangers fans.
O'Neill acknowledged the experience for the younger and newer players but noted that seasoned players like Kieran Tierney, Callum McGregor, and James Forrest have won in similar circumstances.
Next on Celtic's agenda is a home match against Ferencvaros in the Europa League on Thursday evening before they face Rangers at Parkhead in the Scottish Premiership next Sunday.
