Ranieri's team missed the opportunity to move into second position in France's top flight as they had to come from behind to claim a point, while the visitors from Thonon-les-Bains could have won the match with five shots on target to Monaco's two.
Although Monaco had 64 per cent possession, Ranieri believed Evian's chances on goal meant they had more right to victory than his team from the principality.
"Evian deserved more, so it is a good point for us," the Italian said after Friday's match.
"To be honest, if Evian wins the game 3-1, for me that's not a problem, that would have been acceptable.
"We played very badly today."
Evian took the lead at Monaco's Stade Louis II in the 20th minute through Danish midfielder Daniel Wass, while Radamel Falcao equalised seven minutes later for the hosts.
"We played one player against one, facing a strong squad," Ranieri said.
"We hosted Evian after they've just won three games in a row, so they had a lot of confidence in their team.
"They played the game we were expecting, staying tight at the back, waiting for a chance to counter-attack."
