The Danish ace was shown a yellow card following a foul on John McGinn on the halfway line after 36 minutes at Villa Park.
Billing then committed numerous further fouls after being booked before being withdrawn in place of Andrew Surman at half-time.
And Smith believes the Cherries man was fortunate to escape without a red card.
He said: "I think they've had a massive amount of fortune with Phil Billing staying on the pitch.
"He's got booked early in the first half and then he's made a poor foul on Jack Grealish, which wasn't given and then he's made two more poor fouls after.
"He should've been sent off, there's no doubt about that.
"I don't think (referee) Martin (Atkinson) probably had his best game today."