The 26-year-old's £25million move to Anfield from Saints was completed quickly following the national team's early exit from the tournament in Brazil, where they were eliminated after just two matches.
Lallana, who made one start and two substitute appearances in his first World Cup, expects the chastening experience to benefit him and other members of that squad in the future.
"I just have to keep working harder," he said.
"We did suffer disappointments at the World Cup but we need to rest for a couple of weeks, recharge the batteries and then get back to doing what we love which is playing football.
"Hopefully we can learn something from the experience and take it into the European Championship (qualifying) campaign.
"I think you can only become stronger mentally. It is a long way from home in different conditions, a lot of people's first major tournament, and we just have to learn quickly and improve and get better results next time."
Lallana played alongside Liverpool captain Steven Gerrard in Brazil and will now be doing so on a regular basis for his new team.
"There is no limit to what I can learn playing with him. For me to be playing alongside him is quite surreal," added the midfielder.
"He has that aura around him but I need to get used to it because I will be playing with him week in, week out.
"He is still such a good player and can go on to play for a numerous amount of years with the quality he possesses.
"Hopefully I can settle in quickly and I'll give it my best and hope I can add something to the team.
"Hopefully we can win trophies because that is why I am here - for success."