And he added that his wife and children were shouted at in the Spanish city of Seville.
“People have been saying ‘I hope your children die’. I’d like people to put themselves in my shoes and think what it’s like to get threats to my family,” he told the Cadena Cope station.
“My wife and children have come to the stadium in Seville with Morata on the back of their shirts and people have been shouting at them.
“It’s complicated. I understand people booing me for missing chances but there’s a limit.”
Morata, who is on loan at Juventus from Atletico Madrid, has missed a number of chances in the tournament, including a penalty in his side’s 5-0 win over Slovakia on Wednesday.
He was booed by Spain fans in their pre-tournament friendly against Portugal and the pressure has grown after the scoreless draw with Sweden and the 1-1 draw against Poland, where he scored his side’s goal but also missed a chance after strike partner Gerard Moreno’s penalty hit the post.
Morata said he had a sleepless night after missing the penalty in the win against Slovakia, which set up a last-16 tie with Croatia on Monday, but does not regret taking the spot-kick.
He said that despite the abuse and criticism he has faced he feels a huge level of support from his team-mates, adding that former Spain goalkeeping Iker Casillas had called him to lift his spirits.
“I’m proud of the fact I picked up the ball [to take the penalty] after people booed me in the warm-up. A few years ago I would have been devastated but I’m really motivated. Whoever thinks the opposite doesn’t know me,” he said.
“It’s hard to find a group like this especially in the difficult times. After a week like this I’ve been aware of how everyone looks at me but I look in their eyes and see they are supporting me.”