Giggs has taken the post on an interim basis after David Moyes' sacking.
"In the last few seasons, and especially this season, I've seen him stepping in and helping out with the coaching. The amount of respect that the players have for him is unbelievable," Fortune told MUTV.
"I wish Giggsy all the best.
"He's a great guy, an unbelievable player to play with and now he obviously has a different job.
"It was a bit strange to see him standing there like the boss this morning with Nicky Butt alongside him but, at the same time, it feels normal.
"I was driving to training thinking how beautiful it is because he grew up here, he played here - the same with Nicky Butt - and now he's temporary first-team manager. It was a beautiful sight for the club to see those two there."
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