Hull City's 2-2 draw with Cardiff meant a win would have taken the Hornets up but - having had Troy Deeney sent off and seen Jonathan Bond carried off - they were edged out 2-1 by Leeds at Vicarage Road.
In an incident-packed afternoon, goalkeeper Manuel Almunia was injured in the warm-up and replacement Bond was taken to hospital with a suspected neck injury after a 16-minute delay.
Debutant third-choice keeper Jack Bonham was unable to prevent Dominic Poleon putting Leeds ahead, and although Almen Abdi levelled, Ross McCormack's chip slipped through Bonham's grasp in the final minute to win the day.
"It's been a long day and we tried everything," said Zola, whose side will face Leicester in the play-off semi-finals.
"We made some mistakes but we were tired. I cannot tell the players anything. They gave me everything they could.
"We tried everything and they will be okay. They could not make it the easy
way so we will go the hard way, the long one. No one can take away what a
fantastic season it has been.
As to the luckless Bonham, Zola added: "He was very unfortunate with the way he came on. He will have to pick himself up because from these mistakes you can learn."