Dave MacKay's 60th-minute goal gave the Perth side a first win in Glasgow's east end for 13 years. Neil Lennon's team have now failed to score in back-to-back home matches and Rangers are now a point clear of their oldest foes at the summit of the SPL.
"Our front six were a real let-down today," said Lennon. "We were just wasteful in front of goal. We had no cutting edge, we missed chance after chance. The commitment wasn't there today. I don't know where some people's heads are, if they want to be here or not. This can be an unsettling time of year. I'll certainly rectify that in the next couple of weeks.
"I'm not going to pull the wool over anybody's eyes. I'm absolutely raging. I've told the players what I think.
"Some of them come knocking on my door, wanting an opportunity to play. They get an opportunity to play and they fail, they keep failing."
Kris Commons had become merely the latest Celtic player to pass up a penalty opportunity, after three minutes. "I am sick of it," Lennon said. "That would have got us off to a good start. A penalty is a gift and we keep missing them. I don't know how many that is now, six out of nine or something. It's not good enough."
McCoist refused to read much into the Celtic Park surprise. "It is a great day for us because we won 3-0," said McCoist after the success of his Rangers side at Motherwell. "We are four games into the season. There are miles to go. I am just pleased with our result."
Rangers' manager had cause to look at his own situation. Thursday's defeat in Maribor had sharpened focus on McCoist, who has made an inconsistent managerial start. He had presided over two wins in six competitive games before the trip to Fir Park.
"I think before this game one or two questions were asked about the players, the management team and everybody at the club," McCoist added. "It is only one game. We aren't getting carried away but I thought we answered a few questions."
Steven Naismith, Kyle Lafferty and Gregg Wylde scored the goals which saw off Motherwell, who had not conceded an SPL goal before Rangers' visit. Lafferty said he and his team-mates must take responsibility for McCoist's struggles: "I think every player in the team has let him down with the results we've had."
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