The Cod Army headed into the game as League Two leaders but were undone by a late Luke Norris strike for Town, who remain bottom of the table but in much improved spirits after a crucial victory which Aidy Boothroyd will feel they deserved after a number of late setbacks themselves this season.
Alexander had no complaints about the physical nature of the game but was unhappy with the award of the free-kicks prior to Northampton's goal.
"You know what you are going to get here and you have to deal with it and I felt we did," he said.
"You get set pieces and long throws, but we wanted to head it and get bodies in the way and that’s the only way you can defend against that stuff, it’s not tactical, it’s just who wants to win it."