Third-choice goalkeeper Lumley replaced Alex McCarthy after the veteran was not passed fit for Southampton's trip to Amex Stadium.
McCarthy has struggled with a knee problem he sustained before the 3-2 defeat against Liverpool.
He played through that game thanks to pain-killing injections, as first reported by the Daily Echo.
Martin kept the former England international's injury quiet despite knowing on Wednesday that his goalkeeper would not be able to play.
On Lumley's league debut for the club, Martin told the Daily Echo: "I'm proud of him. He deserves it. He's a brilliant team-mate.
Just spoke to Joe Lumley. He is very thankful for his Premier League debut. A moment 29 years in the making. Now he wants more. #SaintsFC
— George Rees-Julian (@rees_julian) November 29, 2024
Brilliant character. It's not like a charity. He deserved to play tonight. Al was struggling with his knee and Lummers is here. He played so well in the Cup last season.
"So I'm really proud of him tonight. I'm really happy for him."
Martin shared more on McCarthy's injury before the game, saying: "Alex played through the pain barrier for us on Sunday.
"He had an injection to play. I love that about Al. He didn't have to do that. His reaction to the game has not been very good.
"He's had a stiff knee this week. He's been unlucky because it happened in training before the game."