Benitez, though, retained hope of avoiding the drop with four of their final six games at home starting with Swansea City on Saturday.
"We have to start winning soon and change a lot of things: the commitment, the passion, the character, the way that we play," Benitez said after his side's lacklustre defensive display at St Mary's Stadium.
"We have to start by winning the first one. If... we score a goal and get the three points... then we'll have more belief and confidence and the players will realise that we can do it.
"At the moment any single individual mistake is killing the team mentally. So we have to be sure for the next one that we will not make mistakes."
Benitez urged the club's fans to stay behind the team.
"The fans will be crucial for us because we need them pushing and supporting the players," the former Valencia, Liverpool and Real Madrid manager said.
"At the end of the season we'll have time to analyse what was going on, but now is the time to stick together."
(Reporting by Simon Jennings in Bengaluru. Editing by Patrick Johnston)
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