The Argentine has been subjected to abuse from the Saints fans for their poor form this morning.
But after they lifted themselves out of the relegation zone with a 3-2 win over West Bromwich Albion on Saturday, Pellegrino thinks the relationship can be fixed.
"Yes, for sure. This is victory is everyone at the club, for the fans, for our employer.
"In our club you must breathe togetherness always even in difficult situations and we try to work together to show we can win games.
"This win, they can enjoy."