Boss Neil Lennon, assistant John Kennedy and 13 first-team players were still self-isolating as close contacts of the injured Christopher Jullien, who was confirmed to have contracted Covid-19 after returning from a training camp in Dubai.
First-team coach Strachan was in charge for the disappointing 1-1 draw against Hibernian last Monday night and again for the visit of in-form Livingston.
Celtic are now 20 points behind Rangers with two games in hand, although the Light Blues quickly get the chance of another victory when they travel to Motherwell on Sunday.
Strachan said: "Obviously the situation isn't ideal but we still had more than enough that we could display a better performance than we did.
"There was certainly a lack of match fitness of certain players which probably means they are not as sharp as what you would like them to be.
"But again the big frustration for me is that we didn't impose our style of play on the game.
"There was a couple of decent performances but probably not so much standout ones.
"The driving force was Callum McGregor. I thought Tom Rogic acquitted himself well today in a completely unfamiliar role as a number nine.
"Tony Ralston came in, he has not really kicked a ball all season. Tony is a very honest and good professional and he gave his all but he tired towards the end.
"It was a tough game, we knew it was going to be. They imposed their way of playing on us more than we did on them."
Asked about the title race, he said: "It is very very difficult. In a normal football season I would say to you that it's going to be very, very tough but the way the world is just now you just never know."
After eight straight wins – six in the league – since taking over from Gary Holt as Livingston manager, David Martindale dropped his first points but found himself in the unusual position of being disappointed that his side did not come away from Parkhead with more.
Lennon, Kennedy and the rest of the self-isolating Hoops will return over the next couple of days and prepare for a rematch in West Lothian on Wednesday night.
Martindale said: "We've been here and got a draw before but potentially we had a fantastic opportunity to get three points today.
"I'll try not to dwell on the negatives. We've come to Celtic Park and got a point, we're still unbeaten and we got a clean sheet.
"I need to watch what I'm saying because we play them again on Wednesday – Lenny will use this in his team talk!
"I thought Celtic had some good chances as well and were a wee bit unlucky.
"But on the balance of play and opportunities created, we were more unfortunate not to get three points.
"No one really dominated the game. On reflection, I'm a bit disappointed but not surprised because this was still a very good Celtic team.
"Hopefully we can make it even more difficult for them on Wednesday."