The Saints claimed a deserve point after holding the champions 0-0 at the King Power Stadium to leave the Foxes 10 points behind Premier League leaders Manchester City.
Charlie Austin hit the post and missed a golden second-half chance when his chip failed to beat the exposed Kasper Schmeichel with Ranieri conceding his side should have lost.
Both teams played in Europe last week as Leicester beat Porto 1-0 in the Champions League while Southampton drew 0-0 with Hapoel Be'er Sheva in the Europa League and Saints boss Claude Puel made seven changes from that game
Ranieri made just one, replacing Luis Hernandez with Danny Simpson, and with the game marking the end of seven matches in 22 days for the Foxes, Ranieri admitted he could have rotated more
"I have to think when we play every three days and maybe at the end of the 22 days it was much better to give some rest to some players," he said, after substituting Jamie Vardy and Marc Albrighton in the second half.
" Southampton played a couple of days after us but they changed seven players and I changed just one, it's not enough but I'm very happy with a point for this reason
"The international break is here but how many players will rest with me? Six? Seven? The others go for their international matches and then they come back two or three days before Chelsea
Then after that we have the Champions League (against Copenhagen)
I have to think about it."
Leicester have at least kept two clean sheets in the Champions League and Premier League since last week's 4-1 defeat at Manchester United and stretched their unbeaten home league run to 19 games.
But they have only won two of their opening seven league games and a second shock title already looks unlikely
Ranieri added: "I recognise Southampton played better than us and they deserved to win
We created some chances but they created more than us
Kasper Schmeichel made two or three great saves, they hit the post and for us one point is OK."
Austin missed a one-on-one with Schmeichel in the second half, his attempted chip failing, having also seen a header saved before he hit the post early on
The striker had netted five goals in his previous four games but could not continue his run in front of watching England caretaker boss Gareth Southgate ahead of the announcement of his first squad on Sunday evening
Puel refused to blame the striker but admitted he was frustrated after the missed chances
"It's easy to see the solution from the bench but he chose another one," he said
"I believe it was OK but it's a shame because there was a situation to finish and take three points
It's important to stay with a good feeling but when I remember the (goalscoring) situations it's difficult to accept
"When you finish a game at Leicester and have a point it's a good thing
It's always difficult to play against Leicester with their pressing and it's very important to keep concentration
We can see a good performance
"Resting players was a positive."
Source : PA
Source: PA