The Hammers were down 3-0 within the first 20 minutes of the clash, and never looked like getting back into it.
However, they fought until the end, and starting from the 82nd minute, scored three unanswered goals to tie the contest.
"Honestly, I can't tell you, it's just one of them special moments in football where it seems like it's meant to be," Rice told Sky Sports.
"Obviously, it wasn't the start we wanted, three goals down in 15 minutes and that's not what we've been about recently. But it still felt like we were playing good football and creating chances.
"It didn't feel like a 3-0 game. For some reason they dropped off us in the second half and didn't try to kill the game off.
"It was a moment of brilliance from Manu and you can see the reaction from the boys – it's something I can't put into words."