Robert Snodgrass's 47th-minute strike secured a much-needed three points for the Canaries against a below-par Spurs side, who lost only their second Premier League match under Sherwood.
Having seen Liverpool beat Swansea City earlier in the day, Sherwood knows his side now has it all to do if they are to qualify for next season's Champions League.
"We’ve just got to get on with our own job," he told reporters. "We can’t rely on other people to lose every game and for us to qualify for the Champions League. It’s not going to happen.
“The gap [behind Liverpool] looks big but we’ve got to bounce back now. We’ve got two games now, the second leg on Thursday then Cardiff at home next week.
"We need characters in the dressing room to do that. It’s the first major setback I’ve had and we’re going to need to be spirited to come back and show what we’re made of.”
Having been in Europa League action in Ukraine on Thursday night, Sherwood refused to blame travelling for his side's sluggish display.
Instead he was left to rue missed opportunties infront of goal, and the performance of Norwich keeper with John Ruddy, as, despite a host of chances, both Emmanuel Adebayor and Roberto Soldado failed to find a way past the England international.
“The first half performance was very disappointing. The second half wasn’t but it was too late, and if you don’t take your chances, which we clearly had, then you’re not going to win," said Sherwood.
“We were strong in the second half so we can’t use travelling as an excuse. First half we looked dead but in the second half we were the far stronger side.
“We have started slowly in quite a lot of games this season. We didn’t against Newcastle and we saw the reward we got for that. Today we were sluggish. It was a nothing game in the first half, neither side did anything.
"We were happy to come in at 0-0 and were hoping to respond, but took a blow early on in the second half going behind to a sloppy goal. We started playing from there. We created a few chances but unfortunately we couldn’t take them."