Spurs missed a golden opportunity to make serious inroads to Manchester City and Manchester United's grip on the Premier League on Saturday when they drew 1-1 at Swansea.
Had they won, they would have headed in to the new year just four points behind both sides with a match in hand.
They still have a good chance to put the pressure back on their rivals this month as they face West Brom, Everton, Wolves and Wigan at home, and Adebayor thinks the home crowd can play a big part in making sure Spurs start 2012 with a bang against the Baggies at White Hart Lane.
"If you want to finish in top four these are the games you cannot lose or draw so it's going to be an important game for us," Adebayor told Spurs TV Online.
"We need the noise, we need them to cheer up, we need the voice, we need them to be our 12th man.
"We have to do everything it takes to take the three points from West Brom."
Spurs started the new year as the top London club in the table for the first time since 1995.
While manager Harry Redknapp maintains a tilt at the title is not beyond his team, Adebayor's main focus is bringing Champions League football back to White Hart Lane next season.
Spurs have lost just once in their last 16 league games but Adebayor has warned that complacency in the second half of the season will cost the team dearly.
The striker said: "We have a big chance to finish in the top four, or maybe even top two or three, but the season will be very long and tough, we just have to keep going, keep believing we can get in that top four, especially now that we have four games at home. We have to focus on them and make sure we get maximum points out of them."
Aside from a 1-0 defeat to Everton on Sunday, West Brom have enjoyed a successful festive period, beating Blackburn and Newcastle while also holding leaders City to a draw on Boxing Day.
Redknapp, who is likely to make changes to his side after playing twice in four days, expects a hard challenge from Roy Hodgson's men.
"It will be a tough game, they have done really well recently," Redknapp said.
"Roy has made them difficult to beat, and they are very dangerous up front."
Redknapp will give a test to Scott Parker after the midfielder came off in the second half at Swansea with a knock to his knee while Aaron Lennon and Ledley King could return from their respective hamstring and knee injuries.