Rice scored a last-minute equaliser for West Ham to take the game to extra-time before Kidderminster hearts were broken by Jarrod Bowen just seconds before the match was heading for penalties.
The National League North side did themselves proud in nearly knocking the Hammers, who are fifth in the Premier League, out of the FA Cup.
Kidderminster manager Russell Penn joined talkSPORT Breakfast on Monday morning and paid great credit to their opponents.
He said: "To lose it with ten seconds to go in extra-time was heartbreaking, but I've got to say this, West Ham were absolutely superb on the day.
"Declan Rice came into the changing room after the game, gave a load of shirts out and even jumped in the same showers as our lads.
"As you can imagine, it was surreal!
"But he was the game-changer, he was superb. He was excellent, there's no doubt he's going to be absolutely massive in the future."
The Kidderminster boss also revealed his conversations with West Ham boss David Moyes and the compliments that were paid to his team.
On reflection about the game, Penn said: "Immense pride at the time and I thought we had West Ham rattled. We spoke to David Moyes in the changing room after the game and said he couldn't see them scoring and had to bring on the big guns to make that happen.
"That's a big compliment to us. We had the pitch, the hostility around the place on our side. We took the game to them, which is what I wanted to do.
Penn added: "He was great. I didn't expect anything less from him, to be honest. He invited us down to the training ground to watch training.
"He's invited us to games and said how well set up we were. On the flip side, he said how well they were prepared and how many games they came to watch us, which doesn't surprise me one bit."