Three days after almost beating Arsenal at St Mary's, the Saints succumbed to a tame defeat against a Foxes side managed by former boss Claude Puel.
The south coast club travel to Stamford Bridge to face Chelsea on Saturday afternoon, and Pellegrino has acknowledged that he has work to do to overcome what he describes as a "surprising" setback.
The 46-year-old told reporters: "It's my responsibility to try to inspire my team. For the last week or so against Manchester City, Bournemouth and Arsenal we showed really good face but this game surprised everyone.
"It was a bad game from the beginning, but as we conceded they got better and our confidence was down."
Pellegrino has won just four of his 18 games in charge since moving to Southampton in the summer.