Douglas Luiz, on his first start for Villa following his £15m switch from Manchester City, scored a consolation for the hosts, finding the top corner with a stunning strike from outside the box.
"We made two big mistakes, they had two goals in 10 minutes and it's difficult to come back from that in this league," Smith told BBC Match of the Day.
"You're always chasing at 2-0 and it allows them to slow it down and kill the game a little bit.
"We kept trying. I felt John McGinn drove the game forward, he had a couple of chances in the first half and we got the goal through Douglas, but we have to be better in possession and its a harsh lesson."