Smith, back in the Millers’ side after illness sidelined him for the 6-1 hammering at Derby, scored the opener before setting up Michael Ihiekwe for the winner on the hour after Lewis Grabban had hauled Forest level in the 28th minute.
Rotherham’s first win over Forest in 23 attempts leaves them a point from safety with six games remaining, and severely dented the visitors’ play-off hopes.
Warne said: “He (Smith) has come on no end. People who come and watch and don’t think he’s a good player obviously don’t understand football.
“It is no surprise that when our best players are here we’re a better team. He played well and was one of many. I thought there were some good performances.
“I am exhausted but over the moon. We rode our luck initially, but I just had a funny feeling it might be our day.”
Warne believes the win has brought more teams into the relegation mix, so increasing his side’s chances of survival.
“The three points were essential and it pulls other teams into it,” added Warne.
“Our lads can’t give much more. How well we are competing and how hard we are to play against is testament to the lads.
“We did see the game out quite well in stoppage-time and frustrated them and got free-kicks. When the referee blew it was a joy. The lads will take confidence from this.”
Rotherham United: Rodak, Jones (Wiles 70), Ihiekwe, Wood, Mattock (Robertson 46), Vaulks, Ajayi, Towell, Taylor (Williams 80), Smith, Newell. Unused substitutes: Forde, Price, Crooks, Vassell.
Nottingham Forest: Pantilimon, Janko (Appiah 76), Wague, Benalouane, Osborn (Joao Carvalho 76), Cash, Watson (Pele 69), Colback, Lolley, Grabban, Murphy. Unused substitutes: Steele, Robinson, Yacob, Ansarifard.
Referee: S Martin (Staffs).