The 46-year-old believes his side's chances of reaching the Champions League group stages hang in the balance after they were held in Eindhoven
The Rossoneri took the lead through Stefan El Shaarawy's header in the first half but were forced to settle for a draw after Tim Matavz nodded in an equaliser following a fumbled save from Christian Abbiati.
Milan spurned a handful of chances to score a priceless second goal, with El Shaarawy and Philippe Mexes spurning good opportunities, and Allegri admits the tie could have been all but wrapped up had his side been more ruthless in attack.
He told Sky Sport Italia:"We struggled a little at the start, losing the ball and allowing them easy chances.
"In the second half we controlled the ball better and above all defended better, as in the first half we were too wide between the sections and that allowed passes through.
"It’s a shame, as we had so many chances to seal the win even after the equaliser, so now it’s all open ahead of the second leg.
"If we had won and especially with a two-goal cushion then we would be looking at this match differently.
"Now we have to think about Saturday’s Serie A opener with Verona and only after that worry about the second leg."