I'm an Arsenal fan so i'm going to defend Rice, but i'm Scottish as well so don't really want England to do well so that tempers a lot of my pro Rice biases.
England just had to many issues going into and throughout the tournament to have the impact that England fans had hoped. Spain don't have the big names any more of the Xavi / Iniesta era, i'd even argue individually are they any more talented in the main than their English counterparts? What they had this tournament is have much better balance throughout the team, they didn't try and force square pegs in round holes.
They had natural width both in full back and further wide areas, they had a 2 holders who knew their roles, a creative 10, they had pace up front that can stretch teams with the wide players, and a focal point up front that came short and ran deep. Guys like Cucurella, Diaz, Morata are hardly world beaters, but they did what was required of them.
England were just the opposite. No natural width at all on the left side. Having to rely on a clearly not match fit Shaw as their only left footed outlet. Kane offering nothing in behind, constantly condensing play. Trying to shoe horn Bellingham and Foden into the same side (they did do a better job of that with the system change). Central midfield partnership constantly chopped and changed during the tournament.
I don't think any individual player, be it Rice, Mainoo, Bellingham, Foden, had bad tournaments. I just don't think the team was set up to get the best out of them. The only individual i would criticise this tournament is Kane, because i honestly thought he was more a hindrance than help, and didn't even do what you want from the basics of a forward player for how England were playing.