Both sides created chances at Ewood Park but the match eventually ended in a 0-0 draw.
Reflecting on the clash, Appleton admitted that a win for either side would have been "harsh".
"It could have gone either way. I thought it was two sides going hammer and tongs with each other," he told the club's official website.
"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."
The draw has left Rovers 10th in the Championship standings.