Lallana continues to build his fitness after a pre-season knee injury as Liverpool struggle to find form, winning just two of their opening five Premier League games.
The England international, who moved from Southampton in July, said playing for Liverpool was very different.
But the 26-year-old said the best way to deal with the pressure was to enjoy the game.
"Just playing for such a big club as Liverpool brings a greater expectation," Lallana said.
"You go into games with a different mentality, you are expected to win a lot more games, teams come to you and camp themselves behind the ball. There are different challenges.
"There is more pressure but it is something you cannot quite explain unless you have experienced it yourself. There is a difference when you pull on that Liverpool shirt to playing for Southampton or any other different team, but it is a great feeling as well.
"There's the fans. You can see the relationship they have with the players here and that is something I hope to build myself.
"The best way to overcome the expectation and pressure is to just try and enjoy your football. You play your best football when you play with a smile."
Lallana said he always expected it to be difficult after his £25 million move.
He believes Liverpool will eventually get back to their best form, and is happy they have shown an ability to grind out wins after edging Middlesbrough in the League Cup on Tuesday.
"We have had a bit of a tough spell but that brings everyone together," Lallana said.
"We ground out the result against Boro and we are going to have to show that side of ourselves at the minute.
"Every team has to grind out results at some stage and maybe we have to show different characteristics, but we will get there.
"I never visualised it was going to be easy coming to a club this big but it's where I want to be. I want to be tested, I want to work and I want to do well."
