Saturday’s 0-0 draw came on the back of defeats to Manchester City and Cardiff, keeping Mauricio Pochettino’s side eighth in the table and bumping them up to 49 points.
Their biggest total since the Premier League switched to a 20-team division in 1995/96 is 52.
They have achieved that twice, in 2000/01 and 2002/03, the latter of which they also finished eighth in, while reaching the FA Cup final.
“It’s always good to challenge ourselves and if we can go beyond 52 then it would be a very good thing for us, so we just have to keep on working the same and we will be there,” said Wanyama.
The midfielder replaced Jack Cork in the line-up for the trip to Villa, starting his first league match since February 1.
Injuries have blighted the second half of Wanyama’s season, but last summer’s £12.5m signing from Celtic was pleased to have made his return to action.
“I’m happy to be back again on the pitch,” he said.
“It has been really long, and also the lads have been doing well, so I’m happy to get a chance to play, and hopefully I will get many chances to play again.
“It’s always good for me to get back on the pitch, and I was looking forward to getting back on the pitch, and I was excited to be back.
“To play alongside these lads, they are very, very good.
“It’s just very nice to play alongside them, because they make it easy also.”
Wanyama, who suffered a hairline leg fracture in December, during the 3-2 home defeat to Villa, said he was suffering no ill effects after Saturday’s game, although he did get caught late by Marc Albrighton in the second half.
“My leg is fine,” he said. “There was a little bit of late contact from the guy – he hit my achilles, so I was a little bit afraid again, because it was the same leg I broke, so I’m happy I’m fine now.”
Wanyama felt Saints deserved all three points at Villa, having controlled much of the game.
“I don’t know what happened and we are just frustrated we couldn’t get maximum points,” said the Kenyan.
“We were really in control of the game and we were hoping to put one in the net, but we couldn’t, so we just have to work hard and coming for the next game we improve.”
Wanyama added: “We had chances to score and we couldn’t score, but we just have to keep on going and work on our finishing, and we’ll improve.”
The 22-year-old also felt Saints should have been awarded a spot-kick, after Ryan Bertrand handled Nathaniel Clyne’s second-half cross.
“We could have had maybe two penalties at least, because there were handballs and the referee decides not to give it. We just have to live with it.”