Villa's build-up to Saturday's home game was marred by the suspension of assistant manager Ian Culverhouse and head of football operations Gary Karsa.
The pair will face an internal investigation, with Lambert replacing the pair on a temporary basis with former player Gordon Cowans and back-up goalkeeper Shay Given, who are both filling joint assistant manager roles.
Villa ended a run of four successive defeats with a much-needed point against Mauricio Pochettino's side, moving them five clear of the relegation zone, and Lambert praised the response of his players and his new staff.
"It's been a hard week, a really hard week," he said.
"The lads have been…I think it has been well-documented, they've been excellent for us.
"When you look at the way they played and the determination there…they stepped up to the plate when questions were asked. As I said to them, I'm proud of them for what they have done today.
"The two lads (Gordon and Shay) have been great. (Youth coach) Gordon, who I know really well…I've always been trying to go to as many development games as I can go to. So I've always played part in that stage of the football club.
"Shay…because I never played him (people think we) had a fall-out. I've never had one cross word. I have always got on well with Shay. I respect him as a goalkeeper and as a guy.
"And he accepted, and Gordon accepted, within seconds (of being asked to stand in). I'm really appreciative of the help."
Southampton wasted a host of chances and felt they should have won a late penalty when Nathaniel Clyne's cross appeared to hit the arm of Ryan Bertrand.
They were left cursing their luck though, and Lambert claimed the point was "huge" in his side's fight for survival.
He added: "(That was a) really tough, tough game and I think sometimes in football matches you get big points and you get huge points.
"That was a huge, huge point for us, considering what's been going on. We had to stop the bleeding (today)…and to get something.
"I thought the second half we were excellent, I really did. I thought we gave as good as we got. We were up against a really good side. I think they're a really good football side.
"(I) didn't think there was much in it. They started better than us and then I think, 15 minutes into the first half, we started to get a foothold in it.
"In the second half, as I said, I thought we were excellent. I thought (Marc) Albrighton (and Gabriel) Agbonlahor were excellent for us. I thought we were great."
‘After Manchester City’s recent form, maybe they’re the underdogs against Manchester United!’ Former Red Devils defender on this weekend’s derby
‘Arteta, Alonso, Emery, me… none of us were physical players – we needed the understanding of the game. That probably helped us move into management’: Premier League boss reveals reasons for natural career progression
