Gary McDonald's close-range finish on the stroke of half-time earned the Shrimps their victory, their second of the season at Spotland, following a 2-1 win in October.
Coleman's side have now won just two of their last nine games in all competitions, leaving the Dale boss furious.
He said: "Morecambe deserved to go through because we were absolutely abysmal and we got what we deserved.
"The fans have paid their hard-earned money to watch the game and they deserved a better performance than that.
"We had three or four players who performed on the night and six or seven players who didn't. You cannot carry that many players."