But the Blues allowed the home side back into it with a 69th-minute equaliser and needed an 81st-minute strike from Rolando Bianchi to secure a win their performance richly deserved.
Bianchi missed a couple of good chances before finding the target late on, while debutant full-back Shaleum Logan fired wide on a couple of occasions, so the Blues should have been home and dry long before Bianchi's winner
"The only thing is that we should have finished the match earlier than we did," said Eriksson. "Bianchi had two chances, Mpenza had two chances and Logan had a couple of chances too.
"If we'd have scored just half of those chances, we could have been three goals in front at least. In football it's always like that, if you don't take your chances, they are always in the game.
"With 20 minutes to go, it's 1-1 and we know that we should have finished it earlier."
However, Eriksson was pleased with the response from his side, which featured 8 changes, after Bristol City drew level.
"It's good to come back and we did that," he added. "Over the last few days I felt that the team would go out and give everything to try to win the game and it was good to see that."