The Saints play Burnley at Turf Moor on Saturday before facing Stoke City, Newcastle United and West Ham United in their three league matches in March.
Pellegrino has acknowledged the importance of their upcoming games, and has called on his players to become "mentally stronger" in the coming weeks.
At a press conference, the 46-year-old told reporters: "I believe in the character, attitude of my team and players. We have to be mentally stronger than before because we will have a lot of stimulus against us.
"The crowd, our behaviour, every single moment will either be for us or against us and we have to be ready for that."
On the club's upcoming fixtures, the Argentine added: "It is an amazing challenge for us. It is an amazing opportunity in all different aspects but we have to think about one week at a time. Now we have to be fully focused on this game and after we will see."
Southampton currently sit in 18th position in the league table, one point adrift of safety.