Neither side could break the deadlock as the Foxes' defence of their league title took yet another blow, with just eight points from their opening seven games.
Ranieri told BBC Sport: "I'm very happy because Southampton deserved to win. They played better. We conceded too many chances to score a goal.
"I recognise they played better than us. Fortunately we finished with a draw from the match."
The result puts Leicester 12th in the Premier League table, 10 points off table-topping Manchester City.