"What meant more to me was not the medal, but my own performance and showing the world that I am a great Boccia player," Smith told BBC Sport. "I think I proved that.
"On the day he was able to get down the court a bit easier and his blasting was awesome. I couldn't quite match that because I am a little bit more restricted than he is.
"The way he throws is very smooth and fluid. It is rare for a BC1 to have that so he takes full advantage of that and fair play to him."
Smith's medal follows David Stone's gold in the T1-2 road race.