Southampton beat fellow strugglers QPR 3-1 at Loftus Road on Saturday and former Saints player Le Tissier feels the club's hierarchy must stick by him, despite their precarious position of 19th in the table.
"I think the fact he has given us back-to-back promotions has earned him the right to have a long crack at the Premier League," he said.
"It is his first chance in the division and he has to be given the chance to grow and learn in the division.
"Hopefully it will be a massive turning point with two home games coming up (against Newcastle and Norwich).
"We have a real chance in those two games of getting out of the bottom three."
Former Southampton manager Lawrie McMenemy echoed those sentiments and highlighted the fact that many of Adkins' players are as new to the top-flight as their manager.
"The thing is not only Nigel is new to the Premier League but the whole team is," he said.
"Any promoted team needs time, particularly ones who haven't been there before.
"Scoring goals has not been the problem, it is letting them in, so the manager would want to sort the defence out."