Saints moved out of the top-flight relegation zone on Sunday as Jose Fonte's late goal earned a 2-2 draw against Fulham.
The south coast club had led against Martin Jol's side, meaning they have now dropped 11 points from winning positions this season.
|8.50||West Hame 8.50 with bet365 to beat Southampton 2-1|
“We have had a tough start to life in the Premier League," he told reporters.
“But the guys in the stands need to stick behind the team. It’s easy to let your spirits drop.”
Next up for Nigel Adkins' men is a trip to West Ham - a fixture they drew 1-1 in the Championship last season.