Danny Rose's first-half header was enough to secure three points for Spurs at the Britannia Stadium in a feisty encounter that also saw home captain Ryan Shawcross sent off.
Though Spurs can mathematically still finish in the top four, they would require Everton and Arsenal above them to lose each of their remaining fixtures, with a spot in the UEFA Europa League far more likely.
"At this stage of the season it's about getting the points," he said.
"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 to go on holiday.
"They still realise there's a job to be done for these great travelling supporters and they will try their best right to the death.
"I just continue to do my job, prepare the players the best I can to make sure they are up for the fight until the final whistle of the season, and if we continue to win then all good."
Sherwood quickly reacted by replacing Rose with Zeki Fryers, and explained his decision post-game: "I thought he was performing really well for us and I didn't really want to bring him off the field, but I had to diffuse the situation.
"I've never heard a crowd so hyped up and I thought I just had to get him off the field and back in the dressing room, out of sight out of mind.
"My heart was in my mouth to be honest. He's still a young guy and still learning his trade. He scored the winning goal today and we're smiling because we haven't been reduced to ten men and he can learn from it."
