In a match that showed plenty of endeavour from both sides, neither team troubled the scoresheet at Ewood Park.
"It could have gone either way," Appleton told Radio Rovers after the match. "I thought it was two sides going hammer and tongs with each other.
"I thought it was a good game to be involved in, but I think Neil would have thought it a little harsh had we got the winner, and I'd have thought it was harsh if they had got the winner.
"In saying that, a 0-0 is not what we both wanted out of the game, but I've told the lads in there, there are 13 games to go and we just have to keep knocking on the door.
"The longer the season goes on, once you get to six games to go, see where you are and then hopefully we are in a position to push on.
"There were a lot of shots at goal, a lot of crosses into both boxes, a lot of good defending, maybe both sides just missed that little bit of composure at the right time."
Rovers are back in action this Tuesday when they travel to the King Power Stadium to face Leicester City. Full ticket details can be found here.