The Scots head into the World Cup qualifier in Zagreb knowing they face a side with talent all over the pitch.
All Strachan can ask of his own players is for them to perform to their highest level and hope they can return with an elusive first win of the campaign.
But he believes that coping with Mandzukic - who netted for Bayern Munich in the Champions League final - will be as tough as stopping Lionel Messi.
He said: "Everybody is aware of Mandzukic unless you come from Planet Zog.
"You know what he does, how he plays. I know what he does but I can't stop him.
"It's all right knowing what he does. It's like Messi. People know what he does but nobody can stop him.
"We will try our best. The longer we keep the ball, then the less chance there is of the other team doing well.
"Whatever team you're playing for, the longer you keep the ball, the less chance there is of the other team hurting you."
He added: "The [Croatia] team as a whole have a good variation in play.
"It's not just short passes; it can be longer passes, it can be crosses. You need to be on your toes.
"With some teams, you know exactly what's coming. With Croatia, they can vary their play, which I think is fantastic.
"Manchester United are a bit like that, they can vary their play.
"I think the Croatian players can play any time, anywhere, in any conditions."
With seven call-offs from the original squad, Strachan has been forced to opt for a relatively inexperienced side for this match.
But he does not feel that too much advantage will be gained from having an unknown quantity against a nation ranked fourth in the world.
He said: "I think they won't change.
"When you are as good as them, you probably decide the tactics of the other team most of the time.
"I've been there myself as the manager of Celtic. I dictated how the game went, really, in terms of attacking.
"We can't work any harder. We can't do any more as a group. We hope we have prepared right and we have put the hours in.
"There will be times - and I'm absolutely sure about that - when Croatia will be dominating the game.
"For all our hard work, we know we are playing against world class players."
On just how tricky a task his side face, Strachan said: "If you asked every other country in the world bar two, they would probably think it's the hardest one you can get.
"It is hard. We are young, the squad is young, but it's good to get used to everything in international football - even this."
The Scots sit bottom of the section with just two points.
Asked what would be a positive result against Croatia, Strachan said: "To get some sort of points from it and for everybody to get back on the bus and say 'I did as well as I could'.
"That's the coaching staff, the players, everybody.
"We couldn't have used the hours any more so they must feel good about themselves because we've left nothing to chance.
"It's a situation where every player must decide whether they are going to have an average game or a good game or a great game.
"I would like to think they will go for great games and, if they can't have great games, they've got to be good team-mates."
With Darren Fletcher, Kenny Miller, Gary Caldwell and Scott Brown all absent from the squad, James Morrison will wear the captain's armband for the first time at international level.
Strachan said: "He's a good player and I think he sets a standard in training.
"He goes about approaching the game in a professional manner. He's a good professional, he's never had any problems.
"He does the right things, he understands the game, he asks questions.
"There were one or two candidates and we went for James.
"He never gets too low or too high and that's crucial when you're part of the coaching staff or the captain."