The Spurs head coach has come under increasing scrutiny in recent weeks, with the situation appearing to reach a tipping point before Monday's Barclays Premier League clash with Sunderland.
The build-up was dominated by a report that claimed Sherwood's tenure would end this summer, regardless of how results went between now and the end of the campaign.
Louis van Gaal and Mauricio Pochettino are favourites to come in but the former midfielder was keen to avoid talking about his future before and after the 5-1 win at White Hart Lane, preferring instead to focus on ending the season with a bang.
"This could have been a sticky game," Sherwood told Spurs TV. "We saw this lot go up to Anfield and Liverpool were lucky to come away with three points.
"We destroyed them tonight, really did move the ball around well and should have scored more goals.
"It is unheard of really and hopefully we can do that in the next five games. We think we can win the next games so let's see where it will take us."
Stoke are the only top-10 side Tottenham face in their final matches, with West Brom, Fulham, West Ham and Aston Villa their other opponents.
Those fixtures would appear to make realistic a points haul that would heap pressure on Arsenal and Everton in the race for the final Champions League berth.
The Gunners currently sit fourth with a five-point cushion over Spurs in sixth, although it is Everton that Sherwood believes are the front runners to end the season in the top-four.
"I don't know [if we can sneak into fourth]," Sherwood said. "You know what, stop thinking about the top four, we're just thinking about winning the next five games.
"Hopefully someone else slips up and they are going to have to do that because Everton have been magnificent, haven't they?
"The way they have built their club and team, they've gone about their business very, very quietly.
"They acquired three loan signings and made themselves a title challenger, really, with the likes of Romelu Lukaku, Gareth Barry - probably two of the best players in the Premier League last season - and Gerard Deulofeu from Barcelona, who could be anything.
"They went about their transfer business fantastically well and they've put themselves in a position.
"I think Roberto Martinez has done a tremendous job so it is going to be difficult to catch them. I think they are going to be the lead runners on that."
While Tottenham are upwardly mobile again, the only direction Sunderland look to be heading is down as the season enters the home straight.
Bottom of the table and seven points adrift of safety, the only glimmer of hope comes from the fact they have two games in hand on many of their relegation rivals.
Sunderland boss Gus Poyet admits they will need a "miracle" to stave off relegation and rejected suggestions their cup exertions have seen them suffer in the league.
"We are where we are because of the cup competitions, because if we had not been on that cup run, we would have been down already," he said.
"That cup run helped us in January, which was our best month.
"That put us in a great situation to take advantage, but as soon as we lost that run, the team went backwards dramatically - backwards in decision making and basic things.
"One of the first things I was told when I came to England was, 'Follow the runners - stop the cross'. How many times did we stop the cross today? What kind of effort did we put in to do that?"