The Saints have endured a testing period in front of their own supporters, with just three wins being recorded from 16 games, and the south coast outfit now face a number of away fixtures in quick succession.
However, Pellegrino has backed his players to respond to having 'everyone against them' as they look to move clear of the Premier League relegation zone.
At a press conference, the 46-year-old told reporters: "It's a nice challenge, my players are ready to compete.
"Obviously away the will be more things we have to deal with, because of the crowd, everyone will be against us. Sometimes the team needs this kind of encouragement."
Southampton are next in action when they make the long trip to face Newcastle United at St James' Park on Saturday afternoon.