Spurs have found themselves off the pace for the majority of the campaign so far, but a 3-1 victory over Swansea City this afternoon saw them draw level with fourth-placed Liverpool, who dropped points against Aston Villa yesterday.
It was Sherwood's fourth win in six matches since being appointed permanent manager of the club, but he admits that his good start would count for nothing if he fails to lead the team into the Champions League places.
"It's been good, we know there are going to be tougher tests ahead, but it's been a good start for me," PA quotes him as saying.
"If the season were to end tomorrow, I don't think the chairman 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 among it."
Spurs face league leaders Manchester City in their next match, which comes on Wednesday, January 29.