The Lilywhites head coach was of the view that his side should have left Ewood Park with something to show for their efforts.
However, a fine header by Ben Brereton Diaz settled the contest and gave Rovers a 1-0 win in the East Lancashire rain.
McAvoy will have been frustrated that North End had 35 minutes to conjure up an equaliser after Brereton Diaz scored, however they created little when chasing the game.
They had a strong shout for a penalty late in the contest though, Josh Earl's cross having struck the arm of Ryan Nyambe.
In his post-match press conference, McAvoy said: "There was one bit of quality in the game which went against us. I didn't think there was much in the game at all between the two teams.
"I think we probably had more of the ball and more of the chances but maybe they had one or two more on target than we had.
"We had an opportunity with Alan Browne bursting through in the first half which came from a great ball by Ched Evans to penetrate in behind.
"The water held the ball up a bit for Alan.
"For their goal it was too cheap of us to allow the cross into the box and we had spoken about not allowing Brereton Diaz or anyone getting across the front of us for a header.
"We had worked hard on that but unfortunately it was a good cross and a quality header.
"I've seen the penalty claim back, it looks like a penalty kick - the lad's hands are away from his body. I don't know why the referee didn't give it.
"There wasn't long left in the game at that stage. That bit of luck just evaded us.
"The conditions weren't great for either team, you could see the beginning that Blackburn didn't want to take any chances in their half of the pitch because there was a lot of surface water.
"I felt we dominated the game in the first half while in the second half Blackburn came out and showed a reaction.
"When they scored the goal they could sit back a bit and the onus was on us to try and push forward for the equaliser.
"We tried to do that but it was a scrappy second half over the piece."
It was a second derby defeat for PNE this season following the 2-0 reverse at Blackpool in October.
Defeat came off the back too of decent results against Middlesbrough and Fulham.
McAvoy said: "We felt we could come here and win the game, having watched them we felt we were a match for them.
"The disappointing factor for me is that again we've had another big following come here to support us and again we have sent them home empty-handed.
"That is becoming frustrating and is starting to p*** me off a bit to be honest."
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