Adkins has done a tremendous job at St Mary's since taking charge in 2010, guiding the club to back-to-back promotions to lead them from League One to the Premier League.
Saints have had a difficult start to the new season, though, and Sunday's defeat at home to Tottenham left them in the relegation zone with just four points from nine games.
However, Adkins does not believe chairman Nicola Cortese will be looking for a replacement in the near future.
"I'll get time from the board," he said. "You need to be confident and positive.
"We're all working hard for each other. We have regular meetings for all employees and I told them that we've had plain sailing in recent years with back-to-back promotions. But this season it is going to be a bit choppy.
"But you have to stick together and come through the storm. Then you say, 'Well done'. It's a great challenge and one we are enjoying.
"No-one said it was going to be easy. This is the hardest league in the world and we are giving a good account of ourselves."