Giggs is in temporary charge of the first team following the exit of David Moyes and Fortune was there to see his former team-mate oversee training on Tuesday ahead of Saturday's visit of Norwich City.
"I just wish Giggsy all the best," Fortune told MUTV. "He's a great guy, an unbelievable player to play with and now he obviously has a different job.
"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.
"It was a bit strange to see him standing there like the boss this morning [Tuesday] 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."
Fortune insists the Reds need to finish the season strongly to give the supporters something to cheer after a disappointing campaign.
"I think the most important thing now is to make sure we win the four games we have left and put on performances that