Although there are just three matches of the season left, Lallana is convinced Liverpool can catch Louis van Gaal's men, but he admits the Reds will have to win all three of their remaining games to do so.
Liverpool end the campaign with games against Crystal Palace and Hull, but their first port of call on Sunday is Stamford Bridge, where they will take on the newly crowned champions.
Chelsea have been celebrating their title triumph this week and they will be given a guard of honour from the visiting team in west London. But after that, Lallana wants Liverpool to take on the role of party-poopers.
"Chelsea deserve to be champions. The table doesn't lie. They have been the best team throughout the season. You have to respect that," said the midfielder, who turns 27 on Sunday.
"All I know is we want to go there and spoil the party. We're looking to go there and cause an upset and put a dent in their celebrations."
United travel to Palace this Saturday and end the season at Hull after hosting Arsenal at Old Trafford.
Van Gaal won all three reverse fixtures, but his team go into the home straight in their worst form of the season. United have lost three league matches in a row for the first time in 14 years.
That has given Lallana hope that Liverpool can catch their old rivals.
"It's not over yet," the England midfielder told Liverpool's website.
"We can still finish in the top four but we need to take maximum points now. We'll keep fighting right to the end. We all know what can happen.
"United have some tough games to play and I am sure they will drop more points.
"We have to put pressure on United by going to Stamford Bridge and getting three points. Pressure is a tough thing to deal with.
"We need to beat Chelsea and Palace and hope it all comes down to the final weekend.
"We all knew that last week was a big week and it was disappointing to only get four points out of the games against West Brom, Hull and QPR.
"We would have been right on their toes, if not ahead of United, if we had performed better. But we still have a chance and everyone believes fourth place is still possible."
Liverpool had hoped to launch another title challenge this season after coming so close last term.
But with three games to go, they are 23 points below Chelsea.
The season has been a frustrating one for the team and for Lallana, who has endured an injury-hit maiden campaign at Anfield.
"It's been really frustrating," said Lallana, who has started just 20 of Liverpool's 35 league games since his B£25million move from Southampton.
"I never really got going and there was no consistency in my form."
The 26-year-old is hoping for a better personal and collective showing next year.
"We've had a couple of tough spells as a team this season but, when you have hard times together, you come out of it in a better place and I believe that will happen here," he said.
"All the new players are going to be better for the experiences of this season. The pressure is always on at a club like Liverpool and everyone has seen that this year.
"It will be a big pre-season for me to ensure I get fit and stay fit. We need a much better start to next season.
"I'm desperate to do well here and contribute as much as I can."