Spurs play at Norwich on Tuesday before heading to Swansea on New Year's Day and then play West Brom on January 3 at White Hart Lane.
Despite failing to overcome Chelsea last week, Spurs are brimming with confidence having lost just once in their last 14 matches to move up to third in the Barclays Premier League.
But with Tottenham just three points ahead of fifth-placed Arsenal, Adebayor knows failure to deliver against three teams they are expected to beat over the coming week could cost the club dearly.
"We have to do whatever it takes to win those games if we are going to finish in the top four. Otherwise, forget about it," the striker said.
Spurs' season started off poorly as they lost heavily to both Manchester sides before recovering to go on an 11-match unbeaten run that propelled them to third in the table.
That run came to an end at Stoke, where they were unlucky not to come away with at least a point after a series of harsh refereeing decisions. They recovered by beating Sunderland and earning a creditable draw against Chelsea, and Adebayor said: "We want to go on another run.
"We have to keep our head up, keep doing our thing, keep enjoying ourselves. Now we are going to play Norwich on Boxing Day. We have to do everything we have to win that game.
"Then we have Swansea away, I'm not saying they are going to be easy games but if you want to be in the top four those are the types of games that you have to win home or away."
Adebayor was been on the end of two disputed refereeing decisions recently. The striker had an effort against Stoke ruled out for offside and a similar decision went against him against Chelsea after turning the ball home in the second half.
The Togo striker has proved a controversial figure at times during his eventful career, but he insists it is important to remain calm when decisions go against him.
"At the moment everything is going against me from the point of view of referees, but that's football to be honest," the 27-year-old said.
"I just have to keep laughing and enjoying myself. We are all human beings. We can't start jumping on referees. He got it wrong against Chelsea, but that's part of football."
Norwich have exceeded all expectations this season, climbing to ninth in the table in their first season in the top flight for six years.
The Canaries are seven points clear of the relegation zone, but Spurs boss Harry Redknapp has warned that they could easily slip in to the bottom three if they have a poor second half.
"Norwich have done fantastic. They have done really well," Redknapp said.
"Them and Swansea have come up and are both playing very well.
"But I'm sure they know that there have been lots of clubs come up and play very well first half of the season and they know they've got to continue that second half, for sure.
"It's going to be tight at the bottom."
Forward Rafael van der Vaart looks set to be in contention for Tuesday's game after his hamstring injury proved less serious than first feared.
The 28-year-old Holland international was substituted at half-time of Thursday's 1-1 draw against Chelsea due to the problem, but a subsequent scan showed no tear and he could therefore be in line to play at Carrow Road.
"He looks okay," Redknapp told Sky Sports News. "He looks like he could be fit.
"We thought he had a hamstring. He went for a scan and it didn't show a tear.
"I think he probably had a bit of cramp in there where he's had a problem before, a bit of tightness he felt maybe might go, so he took the precaution of not playing on with it."