Adkins has been under pressure following the former Championship club's start to the season, which has left the Saints at the bottom of the Premier League table with just four points.
"Whatever team is in the bottom three their manager will be under pressure, or at least the media will think that," said Lallana.
"There has been speculation since the start of the season about who was going to be the manager and ifs and buts, as a player you just get on with it and do as best as you can, not just for yourself and the team but for the manager as well. At the minute and hopefully for the foreseeable future Nigel is the boss and I hope it stays that way."
Southampton go up against West Bromwich Albion this evening.