Neil Lennon thinks the burden of chasing Martin's O'Neill's run of consecutive league wins is weighing heavily on Celtic despite another win.
A 1-0 defeat of Motherwell means they are eight short of the winning sequence during O'Neill's reign.
"We looked a little leggy and I don't know if it is whole mental fatigue of this run," the present manager said.
"But they looked a little tired by the end of the game and that's understandable."
A midweek win over Dunfermline meant Lennon's side surpassed the 18 straight domestic league and cup wins achieved by Jock Stein's Lisbon Lions in 1966.
They now have their eye on the league record achieved while he was a player at Celtic Park.
"We had a great team and people still talk about it," he told BBC Scotland.
"In years to come, I want people to talk about this team.
"It is their record, I didn't want them to let it go today and I'm really thrilled for them."
Lennon was still delighted with the performance in beating a side sitting third in the Scottish Premier League and who had gone into the game unbeaten in their own last six outings.
"I can't speak too highly of the players," he said. "That's 20 wins in a row. It's fantastic.
"The two teams made a great contribution to the game, but I felt we were pretty much in the ascendency for the majority of the game.
"At 1-0, it is always a bit of a worry, but I don't remember my goalkeeper having to make a save of note and I don't remember Motherwell having any concerted period of pressure.
"I thought Darren Randolph made some great saves to keep Motherwell in it, but I thought some of our attacking play in the first half was a little disjointed, but second half some of it was very good."
Lennon had again made changes to his starting line-up to conserve energy with his side now almost assured of the title after reigning champions Rangers were docked 10 points for going into administration.
He praised Georgios Samaras on his reintroduction to the team, as well as Joe Ledley, Charlie Mulgrew and Ki
"My back four were very good," said Lennon, whose side are now 23 points clear of their city rivals after Gary Hooper's winner over Motherwell.
"That's another clean sheet and I thought Samaras had a great second half. Ledley, Mulgrew, Ki played very well.
"Hooper wasn't having the greatest of days but scores a brilliant goal."
Celtic were captained by Charlie Mulgrew, who earlier in the week was named in the Scotland squad, and Lennon explained that it was the defender's hard work that had turned around his career after a disappointing spell with Wolves.
"It is all down to himself," said the manager. "When he first came in, we played him at left-back and he was playing some good teams in Braga and Utrecht and was finding it a little hard to adapt to the pace at that level.
"But, slowly but surely, you could see him develop and get more comfortable within the set-up.
"He could not get in the team because Emilio Izaguirre was doing so well.
"He knocked on the door one day and said 'look gaffer, I'm ready to play'. He didn't shout or criticise and, a week or 10 days later, he played at Ibrox and he's never looked back."