Croatia had two penalty claims waved away by the German official, the second of which came just moments before Jesus Navas scored the winning goal in the 88th minute.
Bilic claimed in the wake of Croatia's 1-1 draw against Italy that referee Howard Webb 'had favoured' the Azzurri, but this time he refused to criticise the decisions made by Stark.
"I do not blame Stark for the result," Bilic told reporters at a press conference. "I have watched all the situations again, Spain's offside goal and the penalty on Vedran Corluka.
"But the referee is human and he makes mistakes, like all others do.
"I do not believe in some conspiracy theory. I do not want to believe in them."
Ivan Rakitic had a clear chance to give Croatia the lead on the hour mark, but his flying header from close range was saved by Spain goalkeeper Iker Casillas.
|23/10||Spain are now 23/10 with Sportingbet to win Euro 2012.|
"Rakitic is a great player," Bilic said. "We had that chance - the best one in that match - because we deserved it. But that was some great save by Casillas.
"Rakitic's progress is huge. From a good prospect he has became a key piece in our team. I would go to war with him, he is a true fighter."
Despite the fact that Croatia gave a good account of themselves at the Euros, Bilic admitted to being disappointed with the team's campaign as he is poised to take charge of Russian side Lokomotiv Moscow.
"Our goal was to advance from this group and win the title," he added. "And we failed. I am disappointed and sad.
"To guide your country's national team, that is the best thing that can happen to a coach. I am proud of my spell here.
"But now I have a new challenge and I am looking forward to it. Maybe I will come back here some time, maybe I will coach Croatia again, but if you ask me that now, I would say no.
"You cannot imagine how much energy this job requires. I spent most of my energy on subjects not related to the team. I beg you [reporters], do not do the same to the next coach."