The 4-0 defeat at St Mary's Stadium was Newcastle third loss in four games, and sections of the travelling support took their anger out on the players as they booed them after the match.
Rob Elliot had kept Southampton at bay for the majority of the first half but Jay Rodriguez opened the scoring in stoppage time, and the lead was doubled early in the second half with Newcastle unable to stop their hosts adding two more before the final whistle.
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Santon had no complaints over the fans' reaction towards the players, and insists they maintain the desire to end the season strongly.
"I understand the fans' reaction at the end," said the defender. "I went over to say thank you, as I always do, and they booed – but I understand because they deserve more from us, and they are right.
"We looked like we played with no passion and we just want the season to finish.
"That isn't true, but we were not good enough. It could have been 8-0 or 9-0, and it doesn't have to be like this."
Manager Alan Pardew, who was in the stands after serving his three-match stadium ban, criticised a lack of effort from his side and reiterated the need to improve his squad for next season.
"Some (players) didn't turn up. Collectively we have to take responsibility for that," said the 52-year-old. "People are going to criticise us and we're going to have to accept that.
"One game hasn't changed our opinion that we need to bring in some players.
"Although the scoreline is poor we've had a positive meeting about taking the club forward."