The high-flying Foxes had won two and drawn one of their opening three games but fell behind in the first half to a Callum Wilson overhead kick.
They eventually found themselves on level terms after Jamie Vardy dispatched a second-half penalty, and Ranieri, after watching his side remain unbeaten, felt a draw was a fair result from “a difficult match”.
“We conceded the goal and until then we were playing well,” he told BBC Sport. “After the goal we slowed down the tempo and had no great personality.
“There were 10 minutes when Bournemouth played very well. In the second half we put them under pressure and made some good chances. I think at the end we deserved to draw.
“It’s important to take one point from a difficult match.
“We have a week now where the players go to their national team and when they come back we must re-start with the same mentality.”