Mulgrew is a left-back by trade but has been used in the engine room by Hoops boss Neil Lennon and Strachan in recent games, and he found himself up against two of the best midfielders in world football when Celtic lost 1-0 to Barca in their Champions League clash at Parkhead earlier in the month.
Asked if that experience had given him the belief that he could play against any midfield, including that of Croatia, whose playmaker is Real Madrid's Luka Modric, Mulgrew said: "Of course, it gives you confidence.
"Different players pose different challenges and playing against the types of players I played against last week, Xavi and Iniesta, the challenge with them is to get a kick of the ball.
"But it gives you a lot of confidence and you have to take that into international football.
"Playing against Croatia, there is Luka Modric and other players like that who are world class.
"That (playing against Xavi and Iniesta) can only help and give you the belief that you can compete with these types of players, hopefully do well and get results.
"In the last couple of games I have played in centre midfield for club and country with Scott Brown but I don't know what the manager is thinking for the Croatia game, we will have to wait and see."
Scotland have no chance of making the finals in Brazil next summer but go into the game on the back of a 2-1 away win over Macedonia and with the knowledge that they beat Croatia 1-0 when the two sides met in Zagreb in June.
Mulgrew is looking to finish the campaign with a double over the Croats with a view to the next qualifying campaign, the 2016 Euros, which will begin next year.
The former Aberdeen player said: "The last wee while has been pretty good so we want to end the campaign on a high.
"It would be nice to finish with a good result and it would give us confidence going in to the next campaign.
"There was a lot of hard work that night (in Croatia). The manager put his ideas across and the team carried them out very well.
"So we have to look to that performance and that result, and other performances, like the ones against Macedonia and even the ones against Belgium and England, to give us belief in the games to come.
"I'm sure the manager will have a formula and he will have us working on it in the days to come."
The big games are coming thick and fast for Mulgrew. The week after playing Croatia he will be back in Champions League action for Celtic.
After losing their opening two games to AC Milan and Barca, the Scottish champions take on Ajax at Parkhead in the first of their double-header against the Dutch side but will go into the game without Brown, who was sent off against the Catalan giants.
Mulgrew admits the loss of his skipper is a "huge blow" but remains confident that Celtic can qualify to the group stages.
He said: "Playing with Scott makes the job a lot easier. He is the captain of Celtic and he plays like that.
"He is a real leader, he makes the job a lot easier and I have really enjoyed it. He will be a big loss but I am sure we will have someone in to do a job.
"We have had arguably the two hardest games so far and you could say we have been unlucky.
"So we have plenty of belief there and as long as it is mathematically possible then we will doing everything we can."