Sir Alex Ferguson's men are favourites to win the group but Celtic defeated United 1-0 at Parkhead the last time they met in the Champions League group stages so must repeat that and attempt to break their long away-day drought in the competition at Old Trafford.
Strachan knows his side have a job on their hands but he is not giving up hope of emulating last season's good run when the Glasgow giants made it to the knockout phase.
"It's going to be right hard work," he said. "We've got a mountain to climb.
"We can play at this level - that was a good enough performance for most places - but unfortunately we were up against one of the best teams in Europe at the moment."
He added: "It was the most comfortable I've been away from home since I came here.
"We worried them when we had the ball.
"I asked the players to go out to perform and I think the first-half performance, plus 10 minutes of the second half, was excellent against a right good side. I actually enjoyed watching a game away from home."
Punters who feel the Bhoys have more to offer in the competition could use their free £25 bet to tip them to qualify for the last 16 and move a big step closer to reaping the rewards should they pull off a double success against the Red Devils.



