Saints are sitting bottom of the Premier League and five points adrift of safety following Monday night's 2-0 defeat away to West Brom.
But Benali insists Adkins deserves time to turn things around, having led the club from League One to the top-flight in two years.
“The club have got to stick with him, given his track record,” Benali, who made more than 300 appearances for the club, told talkSPORT.
“I think he will be the first to admit that he’s made mistakes so far, whether it be team selection or substitutions. But, having seen a few games so far this year, you just can't account for individual mistakes, an error out on the pitch, or refereeing decisions that might possibly go against you.
"I think they should certainly stick with him and, given the chance, I think he will be able to turn things around.
“I think we would all agree that a manager given a good opportunity to prove his worth and get things right on the field is much better than wielding the axe.
“If Nigel Adkins were to be sacked, who are we going to bring in? They are going to come in with their own ideas and beliefs and players they like and don’t like and you are in that vicious cycle of uncertainty.
“I would love them to stick with him, given the record he has over the last few years.”