A goal in each half from sharp-shooter Jordan Rhodes sealed the victory for Rovers, with Appleton just as impressed with the performance of his defenders as they made it back-to-back clean sheets.
"For me I think the most pleasing thing is another clean sheet," Appleton told Radio Rovers after the game.
"If it wasn't for the very late goal in the Brighton game it would have been three on the bounce and I'd have been delighted.
"But if you keep clean sheets then one thing's for sure, you can't lose a game of football and when you've got someone like Jordan Rhodes in your team you always have the opportunity to get a goal.
"It was a solid performance, it was never going to be pretty, we've seen Bristol City two or three times over recent weeks and they do get the ball forward quickly and are very direct so it was never going to be a classic, we knew what we were coming up against.
"Today, and the next 17 games are all about the result, I don't care how we play to be honest, there is a lot of football to be played, over 50 points to play for.
"If we get the opportunity at the end of the season to be around that top six then I'll be delighted.
"Today there was a determination not to concede a goal."
Rovers are back in action at Ewood Park next Saturday when Ipswich Town are the visitors to Ewood Park.
Tickets are on sale now from £15 for Adults, £10 for Seniors and £5 Juniors. Book online today at www.onerovers.co.uk