The 39-year-old was one of four Albion players brought on around the hour mark with his side 1-0 down, thanks to Erling Haaland's first-half opener.
The former Liverpool star scored from the spot in the 67th minute, and then fellow substitute Brajan Gruda grabbed the winner a minute from full-time at the Amex on Sunday.
Following the match, Hurzeler talked up Milner's importance to the team, saying he brings a "special mentality" to the Sussex side.
"James Milner, he always has the belief, no matter against who you are playing, that you can win the game. And if you have these believers in your group, then you spread the belief to others, and then it's like a virus, a positive virus, that goes into the other one, into your teammate, and then also to the crowd," he said.
"I think that's (Milner being a second coach) a good description. He transports my messages, he transports my values in the group, and therefore he proved today he's not only a great leader, but also a player who takes responsibility in the right moments."
Despite not scoring in the Premier League since December 2019, Hurzeler said it was part of the plan that Milner was going to take the penalty.
The veteran has had an injury-hit few years, but the 32-year-old never questioned Milner's quality.
"The decision was clear, so we have clear roles who will take the penalty, and I think if someone can't come back after the injury he had, then you can only mention one person or one player, and that's James Milner," he added.
"His mentality is something special, it's something only real big achievers in life have, and it's something like the mentality inside of him.
"He always has the belief inside of him that he can achieve things he believes in, and therefore, he can be a role model for everyone, not only for football players, but also for other people who have to deal with tough things in life.
"I think you need to talk to James Miller because he has this mentality, this special thing inside that makes his personality so strong."
Milner became the oldest penalty scorer in Premier League history at 39 years and 239 days and the second oldest Premier League scorer behind Teddy Sheringham (40 years and 267 days).
The ex-City player's longevity was on show again after he scored 23 years after his first Premier League goal for Leeds United as a 16-year-old in December 2002.