Santini blamed the result on his defence whose frailty was exposed again by two Croatian goals in four minutes just after the interval.
The champions had to dig deep and equalised through striker David Trezeguet after 64 minutes.
"I hope this result will help the team to wake up," Santini told the after-match press conference. "We took things too lightly after we opened the scoring.
"I don't think we underestimated our opponents. We just failed to respect basic principles when defending.
"If we had Croatia would have found it hard to score goals. I must admit we suffered a lot during the first 20 minutes of the second half.
"When you let your opponents play to their strengths, you can't be surprised if you're in trouble. And it's what we did for a while tonight."
Santini didn't mention any names, saying that he will review the game with the players on Friday.
Manchester United's Mikael Silvestre conceded his and France's second penalty in two games and this time goalkeeper Fabien Barthez, who stopped England captain David Beckham's spot kick on Sunday, failed to make the save.
Veteran captain Marcel Desailly made his return after injury paired with Turin's Lilian Thuram, but their central partnership proved not to match their experience.
A blunder put striker Dado Prso in the ideal position to score his side's second goal.
The draw was a major setback for Santini as France, who beat England 2-1 thanks to two injury time goals, squandered the chance to qualify for the quarter-finals after the second game.
"Apart from the two points we dropped in this match, it's qualifying we missed tonight and that is a disappointment," he said.
"Now qualification depends on playing a good match against Switzerland.
"It's still a bit too early to say but my feeling is that after the victory over England we have relaxed a bit."
