A penalty from Paul Wotton and yet another goal from Crystal Palace loanee Jason Banton had given Argyle a 2-0 lead against the play-off hopefuls.
Argyle keeper Jake Cole made a brilliant reflex save to keep out Junior Brown's goal-bound chest-down in first half stoppage time but he was beaten by David Ball with 15 minutes left but it was too little too late for the Cod Army.
"It was a game going nowhere until we let Plymouth in by conceding a couple of poor goals because of poor defending," Alexander said.
"In the second half we decided to compete properly and we bossed the game after that and created loads of chances.
"But because we were 2-0 down we snatched at those chances and don't put them away. I just thought we were waiting for something to happen instead of making something happen.
"No disrespect to them, we have to come to clubs that are at the bottom of the league and taken games to them.
"I don't think we did that. I thought we just sat back and waited and we got punished. Even at 2-0 I felt we had to improve our attitude and work ethic to get back into the game.
"We scored a goal and had chances after that but games change on chances taken and not taken and I think that's what happened."