Tottenham currently sit fifth in the Premier League after their 1-0 win over nearest rivals Everton at the weekend.
They sit just three points behind Liverpool, who occupy the final coveted Champions League place.
Sherwood has lost just one of his nine Premier League fixtures since succeeding Andre Villas-Boas in December, and believes his side could lose five more matches between now and the end of the season and still make the top four.
“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’ve got left,” he said.
Asked if nine wins from their final 13 games would be enough, Sherwood said: “It could well be. Someone could drop a couple but big rivals like Liverpool are flying and we need them to trip up, that is for sure.”
Sherwood expects the race for the top four to go right to the wire, and hasn’t ruled out tonight’s opponents Newcastle from making a late push.
Magpies boss Alan Pardew wants a strong end to the campaign from his side and said: “We have won more than we have lost – and it’s important that we keep that until the end of the season.
“That gives you a foundation for the year after, where we know we have [transfer] funds available. We have got to just spend it correctly.”