The Austrian oversaw a period of impressive success for the Saints in recent years.
However, he was only in charge from 2018 to 2022, losing his job when the team was in the relegation zone.
Speaking to Fozcast, Ward-Prowse said: "It's a tough one because the list of managers is great.
"The one that probably stands out for me is Ralph Hasenhuttl. He came in at a time that was make or break for me.
"I felt that not only at Southampton but for me and whether I was going to go there or go down - I wasn't really playing at the time.
"He came in and put me on the bench in his first game there, and I didn't get on. In the second game, I came on.
"In the third game, at Huddersfield away, he left me out of the squad - I remember sitting in the dugout thinking that's it, 'I am done'.
"I thought that was me written off with him but in training, I reverted to my work and how I do things to go out and show him.
"The next game was Man City at home, there was an injury so I was playing and after that I played every minute under him.
"His style of play suited me, it was high-energy and there was lots of running. High pressing and getting up the pitch. I think that style really helped me."