Allardyce was appointed as Roy Hodgson's successor after England's poor showing at Euro 2016 ended with a last-16 defeat to Iceland -- a loss Lallana says still hurts him.
The 61-year-old coach has been a mainstay of the English Premier League for the last 15 years with the likes of Bolton Wanderers, West Ham and Sunderland but has faced criticism for the style of football his teams play.
Lallana, though, believes Allardyce's adaptability will improve the national side.
"He spoke to us about wanting to win, which is quite simple really. We haven't gone into too much detail about specific styles. I don't think he has a specific style. He has mentioned how, depending where we are playing and who we are playing, that the style may change," Lallana was quoted as saying by Sky Sports on Wednesday.
"It sounds like a sensible plan for me. He seems adaptable which is a good quality to have when you're a manager. Things have been quite straightforward for me and I have been very impressed with what I've seen."
"Since I've played for England I wouldn't say we have had a specific style. Things change in games and the manager has made it clear to us that he expects us to take responsibility, especially when we are out on the field."
Allardyce's first game in charge comes in Sunday's World Cup qualifier in Slovakia, who held England to a goalless draw at Euro 2016, but Lallana says the squad have to move on from that disappointing campaign.
"We have a new manager, a lot of new staff and a few new players and it is important we start fresh and go on a new journey. We had a good qualifying campaign last time out so we are looking for more of the same," the Liverpool midfielder said.
"I think what happened in the summer is irrelevant. We definitely need to win on Sunday. We are England and, as much as people put pressure on us to win games, we put the most pressure on ourselves to win," the 28-year-old signed off.
