The Premier League champions slipped to 17th in the table and remain just one point above the bottom three after Sunday's 2-0 defeat at the Liberty Stadium.
Ranieri was given a vote of confidence by the Leicester hierarchy this week, but the pressure is growing after a run of five consecutive league defeats.
Leicester have also become the first defending champions to go six top-flight matches without scoring as they still wait for their first league goal of 2017.
But Ranieri retains confidence in his own ability and thinks he is the right person to get the club out of their slump, insisting the players still back him.
"Yes, I think I am still the right man for the job," Ranieri said at his post-match media conference.
"I always question myself but I always say, 'Come on, we can do something good'.
CLAUDIO: "Need to work together to find a solution. When you're not at your max and others are at the top, the battle is difficult." #SwaLei— Leicester City (@LCFC) February 12, 2017
"I think the strength of the man is to have the right balance. Not to be so high when you win; not to be so down when you lose.
"You can remember what we did last season but you need to stay with your feet on the ground and say we have to react together.
"I don't think the players have lost belief. When I listen to them speaking, they want to react and do something better. That is important because I am confident when I listen to these words.
"But we have to find a solution soon."
15 – Leicester City have conceded 15 goals in the 15 minutes before half time this season; the most in the Premier League. Lapse.— OptaJoe (@OptaJoe) February 12, 2017