Saints are now without a win in four games after the Foxes put them to the sword as Riyad Mahrez's strike, a double from Shinji Okazaki and Andy King's goal helped Claude Puel mark his return to St Mary's with a valuable win.
A daunting visit to Chelsea is now on the horizon for Southampton, but Pellegrino wants his team to be galvanised by the prospect of taking on Antonio Conte's reigning champions.
"For us it is a good opportunity this Saturday [16 December] where we can play a top team where we might find more space," he said, according to Sky Sports. "Even against the really good teams you can beat them, in 90 minutes anything can happen.
"We were very close to winning against Arsenal but against Leicester they were much better than us. But this is the Premier League – it is very tough.
"We are thinking about trying to improve and there a big group of teams involved around us and you have to fight for every point.
"The pressure is always [on] with my job. My job is to try and achieve good results and good football. You must be 100% concentrated on the game. We have to choose the players who want to help the club 100%."
Full-back Cedric Soares returned against Leicester after missing the last two games, while Josh Sims is available after returning to training last week.
The 20-year-old has not played since April due to a mystery injury but Pellegrino has a clean bill of health as his side aim to return to winning ways.
"I think everybody is okay, most of them today are training 100%," he added. "Josh Sims came back in to training after seven or eight months. Everyone else seems to be okay.
"Three days before [against Arsenal] we showed a completely different face, and Chelsea is a difficult side but we want to bounce back.
"At this club we are committed to being competitive, and to show our energy. I will try to analyse which players are ready because the Premier League is very demanding."
It remains to be seen whether Chelsea will have striker Alvaro Morata available after he missed the win at Huddersfield Town with a back problem, while David Luiz is certain to miss out due to a knee issue.
Danny Drinkwater was absent from the defeat at West Ham United but came off the bench to play against Huddersfield and could make just his fourth start of the campaign.