Sherwood saw his fifth-placed side maintain the pressure on Liverpool in fourth with a thumping 4-0 victory at Newcastle on Wednesday night, their first win in the league at St James' Park since August 2004.
Liverpool's 3-2 win at Fulham kept them three points clear, but the Spurs manager is confident there will be twists and turns to come.
Sherwood said: "It's very tight. I see it going down to the last month of the season, that's for sure.
"It's going to be tough for anyone to maintain the run we are all having. We seem to be not climbing above anyone at the moment, you are not letting yourself get free in that fourth spot.
"Liverpool are doing excellently and we have just got to make sure we keep breathing down their necks.
"Liverpool are up there at the moment and you would say that they are favourites (for a Champions League place), but we think we can put a charge together. We have got to believe in that.
"We know how difficult it is going to be. But it's not only Liverpool, there are other teams in this race."
Striker Emmanuel Adebayor fired the visitors ahead with 19 minutes gone after Magpies goalkeeper Tim Krul could only parry Nabil Bentaleb's left-wing cross into his path, and that was to prove something of a theme.
Krul could not hang on to the Togo striker's stinging 53rd-minute shot either and Paulinho stabbed in the rebound, and although the Dutchman made a good stop to deny substitute Andros Townsend seven minutes from time, Adebayor scuffed the loose ball past him.
Krul's misery was complete with two minutes left when substitute Nacer Chadli sent a long-range shot across him and inside the far post to wrap up a comprehensive win.
Asked if he could demand any more from Adebayor, who now has nine goals since being recalled to the fold, Sherwood said: "We are always asking for more, but I am not sure we are going to achieve that at the moment. He's at the top of his game.
"He's a real credit to the football club at this present moment in time. He's an example for all our young players to look up to, someone who applies himself on and off the pitch and the training field.
"He never leaves anything on the training field, he works very, very hard and it mirrors that when he steps on to the field."
Sherwood and his players left a wintry Tyneside revelling in a fine performance and deserved victory, but as they headed south, a post-mortem was taking place in the home dressing room.
The defeat was Newcastle's fifth on the trot on their own pitch in all competitions. It was also the club's fourth home loss in succession in the league, the first time they have endured such a run since 1987.
In addition, the last three games have seen them concede 10 goals, score none and fail to pick up a point, and despite the sale of Yohan Cabaye and injury and suspension problems, that was simply not good enough for manager Alan Pardew.
The 52-year-old, who marked 150 games at the helm, said: "I don't want to stand there in my 150th game and watch a performance like that. I don't care about how good Tottenham were, it doesn't interest me.
"They were good, but my team has to be better than that. I am not going to go into any more detail than that.
I made my views very clear in the dressing room. That's where they will stay."
Meanwhile, Sherwood confirmed that midfielder Erik Lamela could be out of action for a month.
He said: "It's not good. He had a thigh strain and he over-compensated and now he's got a back injury. We are hoping it won't be months, but it may be a month or so."