The Italy international believes the Rossoneri need to improve vastly if they want to challenge for silverware this season
The Rossoneri opened the scoring in the 7th minute thanks to a Mario Balotelli strike, but two goals on either side of the break looked to have handed the home side all three points.
However, a late Balotelli goal saw both teams share the spoils, leaving Milan sit in eighth position and Poli fuming that they failed to win yet again on their travels.
"We’re a bit bitter. We should have done more. Livorno played competitive football and showed good rhythm," Poli, 24, told the club's official website.
"If we wanted the win, we should have done just that and even more.
"Now we’ll analyse the mistakes and prepare ourselves for Wednesday [against Ajax] which is a crucial match. The team needs to play at a higher pace like we did against Celtic and Catania."
The Italy international also reflected on the World Cup draw which took place on Friday and is convinced that, despite being drawn alongside Uruguay and England, the Azzurri can be optimistic about their chances at next summer's showpiece.
"Italy have a solid squad and we’ll face any adversary with the right spirit," he added. "It’s a tough group but we’ll be looking to win it."