Celtic manager Brendan Rodgers understood why his side did not reach their peak in a tricky Scottish Gas Scottish Cup tie against Livingston after Cameron Carter-Vickers joined Callum McGregor on the sidelines on the eve of the game.

Celtic reached the semi-finals but it was more nervy than the 4-2 scoreline suggested with Livingston twice equalising through Daniel MacKay and Tete Yengi before Daizen Maeda completed his hat-trick in the 86th minute and substitute Kyogo Furuhashi netted deep in stoppage time.

Celtic again missed skipper McGregor, who hopes to return from an Achilles issue after the international break, and vice-captain Carter-Vickers was left out as a precaution amid concern over the troublesome hamstring which has forced the defender out for several lay-offs this season.

Rodgers was also without the suspended Yang Hyun-jun and injured Luis Palma along with long-term absentee Reo Hatate.

The Celtic boss praised Nicolas Kuhn for his creativity and fellow winger Maeda for his finishing, but added: “We didn’t close the spaces anywhere near what we would want and the speed of our game wasn’t what we would want. But I am understanding of that, some of the guys coming in and also the level of players who were missing.

“The players deserve credit, some hadn’t played a lot, Matt O’Riley was ill all week, Stephen Welsh came in at the last minute, Nicolas had one of his first games. There was a bit of disruption, but the guys got the job done.”

Rodgers admitted Celtic gave away “poor goals”, and added: “I think you see whenever Cam is not in the team – with the greatest of respect – the security in the team.

“I don’t have any fears when we have those guys back. I just think there’s a moment in any team when you are missing your best players then you will maybe not be as tight as you want to be.”

The Celtic manager explained the centre-back’s latest absence.

“We were just going through something very, very light and he made a pass and felt something in the back of his leg,” he said.

“He continued to train but we didn’t want to take any risk whatsoever because as much as he wants to play every game, we had this earlier in the season when he said he was OK and then we ended up losing him for more matches. So hopefully it’s nothing too serious, but we had to take the precaution.”

Rodgers also stated that the level McGregor brings to the game to is “beyond what a lot of our players can do”.

“To be fair, it’s a bit like Jamesy Forrest coming into the game, what a joy to see someone come in for that 25 minutes with that quality and the football idea he brought to the game,” Rodgers said.

“Callum is a player that is important for us, so fingers crossed again we can get to the bottom of that and he’ll be available after the international break.”

Livingston manager David Martindale bemoaned a Joe Hart save from Michael Nottingham’s header at 2-2 and hopes his players can take heart from their display as they bid to overturn a six-point deficit at the foot of the cinch Premiership.

“I’m pretty proud of them albeit we’re out of the cup,” he said.

“It’s been a painful season and we’re on a torrid run. I don’t need self-belief, but I can only hope the players take a wee bit of self-belief.

“I thought they were very good in the game, it would have been easy to come here and accept a 3-0 or 4-0 but they didn’t do that. They played on the front foot and managed the game reasonably well.”