Villa, promoted via the play-offs in May after a three-year absence, head into Saturday’s home game against Burnley third from bottom of the table.
Smith’s side have won only one of their six league games since beating Derby at Wembley in May, but the former Brentford manager said he was pleased with how his players had adapted.
“It’s very harsh because I look at the eight games we’ve played this season and think only Tottenham have been better than us,” Smith said on his club’s official website.
“In all the games we’ve played so far we’ve been very competitive, a couple of mistakes let us down against Bournemouth and at Villa Park we’ve been good.
“We played well against Bournemouth apart from the mistakes, played well against Everton and played well against West Ham.
“But on the road we haven’t got the points we have deserved. Sometimes that’s been down to us and sometimes down to things out of our control.”
Villa, undone by two late goals in a 3-2 defeat at Arsenal last week, play Burnley, Norwich (away) and Brighton (home) in their next three matches, but Smith said he had not targeted them as must-win fixtures.
“We don’t isolate games like that. We’re just concentrating on Burnley,” he added.
“Every game that we’ve gone into we’ve had a belief we can go and win and I think we’ve seen we could probably have won more than we have.
“We’ve got a great belief in what we’re doing and Burnley is our next game. Our 100 per cent concentration is on that game.”
Villa will still be without Henri Lansbury (ankle), James Chester (hamstring), and Jonathan Kodjia at the weekend.
Smith revealed forward Kodjia, who fractured cheekbone when accidentally clashing with team-mate Marvelous Nakamba during training earlier this month, had a mask fitted on Wednesday and could return to contention next weekend.