The Reds went in at the break level with the Gunners but stunned their hosts in the second half to run out 4-3 victors.
Allan scored the second, with Philippe Coutinho netting either side of the England international and Sadio Mane lashing in a solo effort.
And Lallana praised his manager for the turnaround.
“It was a very entertaining game,” he told Sky Sports.
“We didn’t start so brightly after a good pre-season but it’s always difficult coming to Arsenal.
“The manager had a few words for us at half-tim and we responded brilliantly. We got a bit complacent at 4-1, but Arsenal are a top team.
“We want to achieve something special this year we have to be more disciplined as a unit.
“Maybe we showed them too much respect in the first half. We came out of the traps flying in the second half and got the second, third and fourth.
“It was a bit of a tense last 10 minutes on the bench.
“We’ve got huge belief. We’ve got top players on the bench. We’ve got a great squad.
“We’re not in Europe so we’ll have a lot of weeks where we only have to play one game.”