The Croatians will miss the finals for the first time since they started competing as an independent nation in 1991 after Ukraine secured the runners-up spot in Group Six and a playoff berth with a 6-0 drubbing of Andorra.
England, who have 24 points from nine games and were at home to Belarus in their final match later on Wednesday, had earlier won the group to secure automatic qualification for next year's tournament in South Africa.
Ukraine finished second with 21 points from 10 games, one more than Croatia.
Midfielder Ognjen Vukojevic headed in a Darijo Srna corner to give Croatia an early lead, but their celebrations were muted several minutes later by news that Andriy Shevchenko had fired Ukraine ahead in Andorra.
The Kazakhs equalised with a flowing team move in the 26th minute, when striker Sergey Khizhnichenko swept in a good low cross from the right by Yevgeniy Averchenko.
Croatia twice hit the woodwork and the home team's goalkeeper Alexandr Mokin produced a string of superb saves before Kranjcar headed in Srna's cross from the right to give the 1998 World Cup semi-finalists some consolation.
Croatia coach Slaven Bilic said poor finishing had cost his team a place in the finals and declined to answer whether he would stay in charge.
"We will sit down in a few days and analyse the entire situation with the rest of the staff and the FA officials before I make a decision," he told Croatian television.
"We missed a lot of chances today and that has been the story of our qualifying campaign.
"Too many times we hit the woodwork, too many times our shots went just high or wide, our luck deserted us and all I can do is wish Ukraine good luck in the play-offs."
