Ireland appeared fortunate not to give away a penalty in the first half as clumsy challenges in the box by Glenn Whelan and Stephen Kelly went unpunished.
''We were controlling the game in their half, and with a little bit of luck or with a little bit more concentration in the last part of the pitch, we could have won the game,'' Croatia coach Slaven Bilic said. ''If you add the penalty - which was obvious - for us in the first half, I think that we are the ones who should have created a result.''
But Giovanni Trapattoni's Ireland team nearly broke the deadlock before the break when Shane Long saw his header stopped by goalkeeper Stipe Pletikosa.
Richard Dunne missed Ireland's best chance after the break, while goalkeeper Keiren Westwood saved a shot by Croatia substitute Nikola Kalinic five minutes from the end.
''Croatia is a strong team - they are ahead of us in the rankings and they have important players who play in England, Germany, everywhere,'' Trapattoni said.
''We had many missing players and this is a positive result. I think maybe the draw is fair - Croatia had more possession and us less, but each team had only one or two chances.''
''When the players are incisive we can make a difference,'' Trapattoni said. ''In qualifying we have to do this.''
Croatia resumes Euro 2012 qualifying next month second in Group F, a point behind Greece.