Milan are now in 11th place with only seven points from as many Serie A games.
"Of course it's odd to see Milan in the second half of the table. Unfortunately we didn't get a result today despite creating many chances and were penalised yet again from a set play.
"Inter never had a shot on goal other than our error straight after the goal and at the end Palacio," said Allegri.
"I cannot complain about the lads' performance. We just needed to be a little quicker and a little more precise.
"We have to look at the performance and improve some things. It's a shame to lose this way, but we have to accept the result and look at where we got it wrong. At the moment we have conceded seven goals from set plays and that should be avoided. We'll work on it over the break."