The 45-year-old was appointed as successor to Andre Villas-Boas in December on an 18-month contract, but rumours continue to surround his position long term.
Securing a top-four finish would improve Sherwood's chances of him staying on next year, but the former Premier League winner has stressed that he was not set any targets when he took the post.
Asked if he could pay the price if Spurs fall short of their objectives, he told Sky Sports News: "No, not at all. There was never any talk. Obviously we wanted Champions League football, but there was never any pressure or talk about having to finish in the Champions League. Basically, it's just go out and do your best.
"They made a decision that they wanted to make a change and they asked me if I would like the opportunity, and I said, 'If it was right for me'. That's as far as it's gone. That's where we are now.
"I'm doing my best in every game to try and get this team high up the league and I'll continue to do that until the end."