Following Saturday's home defeat to champions Juventus, Inzaghi expected a reaction from his players, but instead Milan slipped behind to two goals from set-pieces in the opening 21 minutes.
Fernando Torres' debut goal before half-time gave Milan something to build on and they levelled through Keisuke Honda midway through the second half.
But Milan had to settle for a point – despite Mirko Valdifiori's late red card for two bookings in the space of 30 seconds – having ultimately left themselves too much to do after a dreadful start.
"Can I explain that first 30 minutes? No, I really can't," Inzaghi told Sky Sport Italia.
"Set-plays have always been a bit of a problem for Milan and once we changed to a zonal system.
"I showed only video clips of Empoli set-plays [in the build-up to the game], as they have been playing with this coach for three years. Maybe the DVD wasn't working.
"It's a real shame, as we would've won if it weren't for those free-kicks. I think it's also an individual issue, as we need to be more determined on the marking."
One major positive for Milan was the contribution of Torres.
Making his first start since joining on loan from Chelsea, the Spain striker scored a fine flicked header from Ignazio Abate's cross and, with increased confidence, looked the most likely source of a decisive goal before he was substituted in the 80th minute.
"I am very happy with my first goal, but the victory would've been more important," Torres told Sky Sport Italia.
"When you face a side like Empoli that play with the heart, it is always difficult, but we had a good reaction and did better in the second half.
"My personal objectives and the team objectives are the same thing: qualifying for Europe. I'll take it one game at a time and try to improve.
"It is always easy to play alongside great players."
