Milan Lalkovic gave the visitors the lead in the 19th minute and they looked like holding out, even after Ben Purkiss was sent off in the 73rd minute for his second yellow card of the afternoon.
But Rotherham finally came good in the 88th minute when Alex Revell headed on for substitute Nicky Adams to slam in the equalizer off the underside of the bar.
Smith said: "It was a really good performance, we deserved to win the game and a cruel deflection at the end has cost us.
"It was a more spirited performance from us and that's what we're about. I thought we were excellent. We scored a goal and outplayed them in the first half.
"They put us under a lot of pressure for the last 10 minutes of the first half and in the second half we have had to defend a lot of balls into our box and I thought we were fantastic at doing it. It was cruel at the end.
"I thought some of our football was terrific in the first half and we opened them up from a great move and it was a really good finish.
"I've nothing but praise for the players probably nobody gave us a chance coming here with the run they are on but we were very good. You have to come to a place like this and be defensively spot on."