The Young Lions defeated Venezuela 1-0 in the final to claim England's first World Cup trophy since 1966.
And Unsworth, who coaches the Toffees Under 23 squad, could not contain his delight.
"It's an amazing achievement," he told the club's website.
"What they have done is very, very special. It probably hasn't sunk in just how special it is yet. I played in [an Under-20s World Cup] myself, so I know it is so difficult to win a competition like that, with the talent and great teams you have to get past.
"We are so, so proud of our Everton boys. I am delighted. I was biting my nails and shouting at the TV, then I was jumping around at the full-time whistle. It was a great team performance and the lads dug in when they needed to.
"It's a very proud day for Everton because for those lads to represent our Club in the way they have done is just fantastic."