City captain Vincent Kompany said Pep Guardiola's side "ran out of steam" after Johann Gudmundsson struck in the 83rd-minute to snatch a point.
The Premier League leaders had gone ahead through Danilo's long-range beauty and saw several chances to consolidate their lead pass by, none more gilt-edged than a Raheem Sterling miss from barely a yard out.
City remain in the hunt for silverware on four fronts this season, having progressed to the EFL Cup final and through the last-16 in the FA Cup and Champions League, with Guardiola using a rare free week to relax.
He told a news conference: "Time off for everybody, officials, doctors, nobody in Manchester!
"If a game is in three days we're going to play in three days but we have until the next Saturday [when they host Leicester City].
"We'll have three training sessions before Leicester and Basel and I think it's good for everybody to rest a bit because we've had, since August, just one midweek off.
"So, we have a lot of games and the way we played today... I decide to give [everyone] three days off."
Guardiola expects defender John Stones to be one player to benefit from the time off, the England defender having missed City's last two games.
"He had a problem in the knee," Guardiola explained. "I prefer to rest to recover because the last period before the last game he was sick but before that he had a little pain in the knee.
"I decided we had Vincent come back and Aymeric Laporte is already here, so I decided not to use him today to recover.
"These 10 days [he can use] to come back better. He should be good for Leicester and Basel and the next games."