The Saints have struggled to score goals this season, and have managed just four in their opening six games.
"We have to improve our overall play in the final third," said Pellegrino.
"We need more character, belief and instinct - and we need more bodies in the box.
"But it's the most difficult thing. How many chances did Manchester United create against us, and they've got a player with quality, a massive player, and they score once. But that's football."