Interim manager Neil Lennon says Celtic's display in defeat by Rangers "was unacceptable" and suggested the home side "wanted it more".
The 2-0 reverse was a first domestic defeat in 16 games for Celtic, who retained the league title last weekend.
"The better team won," Lennon told Sky Sports. "We lacked energy and we looked tired today. I don't know if it's mental or physical fatigue.
"We weren't at the races. We got beaten and deservedly so."
Second-top Rangers went ahead through James Tavernier after only two minutes and Scott Arfield added the second after half-time at Ibrox.
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"We were looking for a reaction even at half-time and didn't get one, so they've got to have a look at themselves," Lennon said.
"But we've got a good group in there and they've let themselves down today."
Lennon had rested Scotland left-back Kieran Tierney, who will need a summer double hernia operation, ahead of the Scottish Cup final against Hearts.
The two sides also meet in the final league game of the season at Celtic Park next Sunday.
"I don't think they'll need much picking up," Lennon said. "They'll know they have a huge cup final looming in two weeks time and there may be places up for grabs, so that should be motivation enough for them.
"That performance was unacceptable even though they've been brilliant for a long period of time. It just seemed like Rangers wanted it more today than we did. I think that's the biggest criticism we can aim at the players."
Lennon was particularly unhappy at the opening goal as Tavernier's in-swinging free-kick evaded the heads of both sets of players and deceived goalkeeper Scott Bain.
"It was sloppy from us," he said. "First of all to give the free-kick away then for the players not to be in the positions that they're supposed to be in.
"They switched off and and you can't switch off two minutes into a game. It's a quality ball in and then if we had the personnel in the right positions then we would have dealt with it better. But that sort of summed up our day - we were just sloppy and lacking energy and hunger."