Villa remain four points from safety with four games left ahead of Sunday’s visit of Crystal Palace, with Smith still backing his players to survive.
He said: “They are all big games. Every Aston Villa fan in their hearts didn’t expect too much from Liverpool and Manchester United, but there is an awful lot of belief in the dressing room.
“We know the last four games are going to be very big and we have to be very competitive in those games. They are not in top form that Liverpool and Manchester United are.”