Paulo Dybala struck the winner deep into injury time for Juve.
“This is football and it can be ruthless," shrugged Inzaghi.
“There were 20 seconds left, we were almost perfect and allowed Juventus nothing. There is disappointment, but I complimented the lads anyway, because they gave their all. Unfortunately, football is down to incidents."
Lazio understandably ran out of steam late on, having played 120 minutes and a sudden death penalty shoot-out against Milan in the Coppa Italia on Wednesday.
“I have to say, you really couldn't tell. We were giving the impression of getting a goal, then Dybala did well, but the ball went between many legs.
“Now we've got to leave these two big disappointments behind us and start again. We certainly didn't deserve to lose, so we must build on the performance.
“There's a long way to go in the race for a Champions League spot and we'll see what the verdict is come the end of the season."