Falkirk boss Ray McKinnon criticised referee John Beaton in his after-match comments, while rival Jonatan Johansson was delighted with a first win.
MATCH REPORT: Morton 1 Falkirk 0
Bob McHugh's late strike gave Morton all three points in a scrappy contest that boiled up just after half-time with the sending off of Leo Fasan, and then a clash in midfield involving Paul Paton and Jim McAlister.
But it as the red card, and the reasoning that irked McKinnon, who came under fire from the home support after leaving Greenock just three months into his tenure.
He said: "I've just looked at it back there and we are disappointed because the referee has said to a goalkeeper he can't handle it outside the box, but he hasn't handled it.
"He has fouled the player, there is no doubt about that, but our other player is in a good recovery position so it should only have been a booking - he has got that wrong disappointingly and made the wrong comment to a goalkeeper.
"But that sums him up today, I think he was pretty poor overall.
"For the goal they took a free kick with the ball rolling, it had to be a deadball its a rule.
"But congratulations to Morton. We worked extremely hard and the guys gave everything especially playing with 10 men for 45 minutes but we just need to go again and keep working hard and working towards three points."
HOW IT HAPPENED: Morton 1 Falkirk 0 LIVE
His opposite number Jonatan Johansson was delighted with his first win since his switch from Rangers.
He said: "We haven't played badly but we haven't managed to get a win and three points is massive in this league. I know what football is like it sometimes takes time but the team is very together and we've got that first one now.
"People think automatically because a man is sent off it's going to get easier but they drop deeper and defend with the same amount of players they just don't have the same attacking threat. I tried to tell the players to play the same way and keep it going not to change, keep it going.
"It was great to see Bob on the scoresheet he has been frustrated in the past few weeks and I have been trying to keep him happy so this was great for him to come on and score."