The Welsh side have made a strong start to the campaign but they were a distant second best at Spotland where goals from Peter Vincenti, Graham Cummins and Bastien Hery lifted Keith Hill's squad up to fifth in the table.
The visitors saw a spot kick saved by Josh Lillis in the second half at 2-0 down, but Edinburgh admitted they did not deserve a route back into a contest dominated by Rochdale.
"That was very disappointing, but we were certainly beaten by the better side," said Edinburgh.
"In all aspects of the game we were poor. We were poor in possession and poor out of possession.
"It was unlike my group of players, but maybe it will give them a wake-up call and bring them back down to earth. We have had a fantastic start but if we start thinking we are better than we are then this is what happens.
"I thought all three goals could have been avoided and once we had given them a heads up we didn't really deserve to get back into the game.
"The penalty might have changed that but I think sometimes you just have to give the opposition credit and I thought they were probably the best side we have come up against this season.
"We found it hard to get the ball off them and they passed it very well and caused us problems. But we were off the pace."