The 3-1 win over Swansea on Sunday moves Spurs up to fifth, level on points with fourth-placed Liverpool as Sherwood, who opted against sticking with a 4-4-2 formation, remained unbeaten in the Premier League since taking over from Andre Villas-Boas.
It is his fifth win in six matches and Sherwood, who admitted Swansea should have had a penalty for Dawson's push on Bony when the game was goalless, has been delighted by his start as Spurs boss since signing an 18-month deal.
But he is in no doubt as to what is expected of him when it comes to the London club's finishing position.
"It's been good, we know there are going to be tougher tests ahead, but it's been a good start for me," he said. "If the season were to end tomorrow I don't think the chairman (Daniel Levy) would be too happy because we are fifth.
"The final league position has to meet the expectation of the club otherwise it's 'goodbye Charlie'.
"The club needs to finish in fourth place, we want to finish in fourth place. Anything other than that will be a disappointment but realistically we should be in amongst it."
Adebayor has now scored six goals in seven appearances under his new manager, but Sherwood insisted the striker's revival is not down to him.
"I haven't said anything to him, I have just given him the stage to play on, he hadn't had that stage for a while," said Sherwood. "I haven't made Emmanuel Adebayor a good player, I think we already know he has been a good player at every club he has been at.
"We just needed to get some consistency out of him and I am sure if he continues to enjoy playing he will keep performing well.
"He is enjoying it, if you enjoy yourself playing football you will get the best performances out of yourself.
"He is no different to anyone else. He has a smile on his face, is scoring goals and is enjoying it.
"We are trying to encourage the boys to roll the ball into him because he makes things happen. He dictates the pace of the game for us and he likes to get it wide as he knows there is a chance he can score from the cross.
"After his first goal he grew even more and started dominating the game for us. But there's been no magic wand from me. He has always been a good player."
Swansea boss Michael Laudrup, whose side have now gone eight league games without a victory, said: "Again, great attitude, put them under pressure, had a couple of good chances... and then the first time they have a shot on target they score.
"But it's something that happens when you're a team that is struggling a bit. It's not our moment and things like that happen.
"I think we have to admit that we have some problems right now, we haven't won for quite some time, but on the other hand we just have to continue like this.
"I think the only thing we need is a success, that means a win in the league, and now we just have to move on."
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