Mario Balotelli's first Premier League goal for Liverpool guided Brendan Rodgers' side to the key win at Anfield, seeing them close the gap to sixth-placed Tottenham to a point.
Lallana set up the match-winner after coming off the bench, and he has set his sights on a top-three finish with his side on a nine-game unbeaten league run.
The 26-year-old believes the return of striker Daniel Sturridge, as well as improvement from the club's off-season signings, should have them eyeing third place.
"That's a massive three points for us," Lallana told the Liverpool Echo.
"We're only one point behind Tottenham now and we have got everything to play for.
"We can go higher than fourth, we can hit third place. We've got Daniel Sturridge back now and it was great for him to get through 70 minutes.
"I was itching to get on tonight. It was a great game and a great atmosphere and against my old gaffer [Mauricio Pochettino] who I have a lot of respect for.
"It was end to end and at times it could have gone either way. It was nice to get on the pitch and contribute to the result.
"I'm pleased for Mario and that goal will be great for him. He needs to keep working hard. If he does that and keeps putting the effort in then the goals will come."
Rodgers' off-season signings had been questioned, with the majority struggling to settle into his team.
But the likes of Emre Can and Lazar Markovic in particular have improved, and Lallana said he never doubted the signings would eventually step up.
"We've got a great squad and we're gaining momentum," Lallana said.
"We were missing Raheem [Sterling] tonight but Lazar came in and got his goal.
"You look at the likes of Lazar and Emre, a lot of the new players are settling in well and we're seeing that out on the field.
"People were questioning the new signings at the beginning of the season but not for one minute was I questioning them.
"It was always going to take a little bit of time as they're young players. Now they've settled in we're starting to see the rewards."
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