Spurs are currently fifth in the table following their 1-0 win over Everton on Sunday, just three points behind fourth-placed Liverpool.
Sherwood has lost just one of his nine league fixtures since replacing Andre Villas-Boas as head coach, albeit a 5-1 rout by Manchester City, but feels he could afford to see his side lose several more games in the run-in.
"I haven't looked at it, maths isn't my strong point but I would say we can only possibly afford to lose four or five games maybe of what we have got left. That would be a huge tally," he said ahead of Wednesday's game at Newcastle.
When asked if nine wins from their remaining 13 games would be enough, Sherwood replied: "It could well be, no one is dropping points are they. Someone could drop a couple but big rivals like Liverpool are flying and we need them to trip up, that is for sure.
"We're looking upwards rather than behind us but we know it will be tough and there are teams behind us capable of putting a run together and sneaking fourth.
"It will go to the wire. I don't think anything will be secured until the last month of the season. I would say Newcastle have to consider themselves in it and possibly Southampton, Manchester United for sure.
"Our target is fourth place and it always has been, if we can get higher than that then great but it is the target we are looking for."
Sherwood signed an 18-month contract when he replaced Villas-Boas in December and, although he does not know if a fourth-placed finish would keep him in a job, he is certain the club is big enough to attract top talent even if they end up in the Europa League once again.
"I just need to get as high up the league as I can. If my achievements don't match the expectations of the club then I'll be gone," he said of his own future.
"The expectancy will always be there with the fans, and rightly so, we have spent a lot of money at the club.
"Tottenham is a massive football club and will always attract the biggest named players. If they are coming here to build and progress with the side, they are going to pick Tottenham.
"There are other clubs where they could go and sit on the bench for a period of time and pick up Championship medals but it isn't something I would have wanted to have done.
"The club sells itself, it is far bigger than any manager. I'm not here making out I'm doing anyone a favour being Tottenham manager. If the players want to come they will come.
"They know full well what we have here and what we have to offer and if the be all and end all is Champions League football and we are not in it, they have to make a decision."