The Portuguese was sacked less than 24 hours after last weekend's 5-0 humiliation at the hands of Liverpool, with head of football development Sherwood handed temporary control.
Sherwood's first match at the helm resulted in a Capital One Cup exit to West Ham, but on Sunday he oversaw his first victory with an attack-minded display at Southampton.
Emmanuel Adebayor netted either side of a Jos Hooiveld own goal as Spurs ran out 3-2 victors, resulting in bookmakers immediately shortening odds on the former midfielder being handed the reins on a permanent basis.
The win will certainly not do those chances any harm and Sherwood hopes to take control of the Boxing Day clash with West Brom with a clearer idea on his future.
Asked what happens next for him, Sherwood said: "Ideal for me is to have a chat with the chairman and see what's best for the football club moving forward.
"I need to know what they're thinking moving forwards. I don't want this job for five minutes. That's no interest to me.
"It is either are we going to move it forward or not? That's where we are.
"There are some great candidates out there for this job. It's a massive club with history and tradition.
"It is fantastic, a great honour to represent them, but it needs to be right for me and, first and foremost, right for the football club.
"I need to talk to the chairman and see what he's got planned. I'll see him tomorrow because I'm in at the training ground. I'm sure it won't be before that."
Former Tottenham and England boss Glenn Hoddle is second favourite among bookmakers for the post - behind Sherwood - and confirmed his interest in the job before the match, while Frank de Boer and Louis van Gaal continue to be mentioned as potential appointments.
"Whoever takes this job is in a good position," Sherwood said. "Andre has left the club in a good state, to be honest. There's nothing wrong with the job he's done.
"If you look at the league table, we're right up there. We're also in the European competition next stage.
"You can't knock what he has done at the club, but it is just up to someone now to take it on and hopefully take it onto the next step."
If Sherwood ends up only being at the helm for a short period, whoever comes in will be thanking him for rejuvenating Adebayor.
Having been cast aside by Villas-Boas, the Togo striker has scored three goals in two starts under the interim manager and was superb throughout at St Mary's.
"Listen, we all know Adebayor, we all know he's a top player," Sherwood said.
"He doesn't need any motivating to go and play now because he's not played for a long time. He's a top player and is certainly warranting his place in the team at the moment.
"I've not said anything to him. Nothing. It's down to him.
"I've not had to gee him up. All I've said is: 'There you go Ade, you are going to and play and I want you to attack. I want the defenders to defend and the midfielders to play in midfield. Go out there, crack on and do what you do.' It's a simple game.
"That's how I've always viewed it; it's about getting the ball to your top players in the right areas of the field. That's what the players did with us."
The victory stops the rot at Spurs, but continues Southampton's frustrating recent form.
Saints, who took the lead through Adam Lallana and made it 2-2 through Rickie Lambert, have now gone six matches with a win - hardly the best preparation for trips to Cardiff and Everton.
"It was very frustrating, we are very angry about the result," said manager Mauricio Pochettino, who has been linked with the vacant Spurs post.
"We actually dressed up as Santa Claus today and gifted them so many goals and so many chances.
"We started off quite well in the first half, we got the 1-0 and we were very close to getting the 2-0 but then when we conceded the equaliser it was very hard to get back in the game, especially in the second half it was very tough."