Cucurella enjoyed an outstanding tournament with La Roja, despite being written off before it kicked off by Neville.
The former Valencia coach stated: "He's not been convincing at Chelsea. He's played a few games towards the end of the season.
"He's aggressive, he's tenacious, he's a busy little full back. The price tag still astounds everyone to this day.
"The Spanish defence, it's got a lot of experience now but there's something just missing from Spain that makes you feel like they're going to go all the way. I have to say that him being at left back is a good example of why we think that."
After last night's celebrations, Cucurella posted a picture of Neville's comments with the caption "We went all the way Gary. Thanks for your support."
