Lambert called upon his new signing when Adam Drury pulled a hamstring during the warm-up at Ashton Gate.
"I've waited for a few months. I really enjoyed the game and the result helps that," Smith told BBC Radio Norfolk.
"I saw Adam go down in warm-up so I knew I had a chance of playing.
It was just good to get some decent minutes under my belt in a proper match
"Then I found out at about two minutes to three when I came back in from warm-up and the manager told me I was playing," the former Rangers defender added.
And despite being substituted with 10 minutes to go, Smith said his first start of the season had come at the right time.
"I played 90 minutes for the reserves during the week which helped me. That was the first 90 minutes I'd played in about four or five months.
"It was just good to get some decent minutes under my belt in a proper match."
Source: BBC Sport