Spurs still have an outside chance of finishing in fourth place, although it is much more likely they will qualify for the Europa League rather than the Champions League.
Danny Rose scored the only goal of the game in the 33rd minute - his first for Tottenham in four years - to hand Stoke just a third home Barclays Premier League defeat of the season.
Sherwood's future is in serious doubt, but the Spurs manager is determined to make sure the club finish the campaign as strongly as possible.
He said: "At this stage of the season it's about trying to get the points. It can't always be pretty, sometimes you have to dig in and work for each other and I thought we certainly didn't look like a team who had their sunglasses and flip-flops packed ready to go on holiday.
"They've realised there's still a job to be done for the great travelling support that we bring and they will try their best right to the death.
"We've got two more games. We go away to West Ham, which is a derby that we need to win, and then we come home and we're going to send them away happy after beating Aston Villa in the last game of the season. That's what the plan is.
"I continue to do my job, prepare the players the best I can and make sure they are up for the fight right until the final whistle of the season. If we continue to win, then all good."
Tottenham had a man advantage for the final 38 minutes of the match after Stoke captain Ryan Shawcross picked up a second yellow card for a foul on Rose.
But the hosts responded to the crowd's sense of injustice and finished the game looking much the stronger team.
Sherwood said: "It's a tough place to come, and we knew that. They've taken some big scalps here, they've only been beaten three times, and probably on everyone's coupon this was a banana skin, but it never looked like that.
"We should have come in at half-time more than two goals up. We dominated the game. I said to the players at half-time to be a bit more patient on the ball, a few more forward runs and we'll create something, but it seemed to give them the initiative after they went down to 10 men.
"The crowd were fantastic, drove them on, and we had to fight it out. But there were some good performances.
"The criticism of Tottenham teams in the past sometimes was they didn't want to fight it out but this team don't roll over and they're willing to put their bodies on the line for the cause. I demand nothing less than that."
Stoke had hoped to reach two club milestones of five home wins in a row and 47 points, equalling their best tally for a Premier League season.
Surpassing that mark and achieving a first top-10 finish have been major targets for the Potters throughout the season, but they have work still to do in their final two games against Fulham and West Brom.
Manager Mark Hughes was proud of the showing his players produced in adversity but was left ruing a failure to make the most of their opportunities.
He said: "We had any number of chances that we could have created when we went down to 10 men, and that's the disappointing part because we put in a great performance and had no reward."