A rare goal from captain Wes Morgan was enough for the Foxes to continue their seemingly inevitable road to the Premier League title, but Southampton were in the game and felt aggrieved not to have been given at least one penalty.
The Saints' loss meant that Ronald Koeman's side dropped further behind the race for the top four, and are currently sitting in seventh.
However, Europa League qualification is still the aim with Southampton enjoying a goal-difference advantage over eighth-placed Stoke City and a two-point buffer between themselves and Liverpool, who are ninth.
Cédric says Southampton will continue to fight
Speaking with the club's official website, Cédric claimed that the team "always look up", and are "fighting for a place in Europe".
"We fight every game to achieve the best result," he continued, noting that the team would continue to take each game as it comes and hope for a positive outcome at the end of the campaign.
The 24-year-old, who has nine caps at senior international level for Portugal, said that the squad had been disappointed to find themselves coming out of the Leicester game with nothing after creating a number of chances against in-form opposition.
Despite the obvious disappointment of three points dropped, however, Cédric said that he could "have a clear mind and not be too upset" after the game as he and the rest of the squad had "given [their] best".