The French right-back was handed his first league appearance by manager Mark Hughes at home to a Manchester United team that included Paul Pogba, who had lifted the World Cup for France five months earlier.
"I didn't think, 'It's Paul Pogba', I just tried to play my game," Valery said after receiving his Premier League Debut Ball.
"It was amazing because everyone knows it is one of the biggest clubs in Europe and even in the world, and there are big French players.
"It was a big moment for me and my family."
The defender, now 20, joined Saints from Rennes in 2015 and had won his place at St Mary's Stadium after impressing in Premier League 2.
Valery finished 2018/19 with 23 league appearances and two goals, including a sensational strike at Old Trafford.
The Paris-born player is grateful that a manager battling relegation stuck by him.
"I am so thankful for everything he has done for me this season, he gave me his trust even after I made mistakes," Valery said.
"I don't think there are a lot of coaches who would have done that, so I just want to give everything I have got for him."
Hasenhuttl says he put his faith in Valery after seeing his work on the training ground.
"The first thing you see is the unbelievable physical options he has; he is very quick," the Austrian said.
"The second thing was more self-confidence with every game and finally he scored twice against big teams.
"What no one sees is he is working nearly every day, if he is off, with our coaches."
This desire to work hard for the club is a result of the support Southampton gave him when moving to England as a 16-year-old.
"When I came from France I couldn't speak English at all," Valery said. "That was the hardest bit.
"When I had problems, because my family's not there, everyone at the club helps you, they're there for you.
"This club is like a family and it's good for young players to be a part of that."