The Saints have struggled upon their return to the Premier League and currently sit in the relegation zone after conceding 24 goals in just eight games so far this term.
Southampton were smashed 4-1 at West Ham on Saturday, with all goals scored in the second half and Adkins bemoaned his side's defensive frailties.
When asked if he would be given time to turn the team's form around, he told reporters: “I don't know. That is football, I am being brutally honest with you.
"There is a vision at the football club to play a certain brand of football by passing the ball.
|SAINTS UNDER PRESSURE|
|4/1||Southampton are 4/1 with PaddyPower to finish bottom of the Premier League this term|
"You've got to keep it out at one end and stick it in at the other end.
"On too many occasions this year in the Premier League, we've not kept it out of our net and I am being upfront and honest with you.
"There needs to be stability at any football club, which is important. But I am not naive as it's football and football is a results-driven industry.
"We've got a process in place that we're doing our best to adhere to, but you've got to win games of football."