Luke Murphy's strike proved to be the difference as the Railwaymen saw off a spirited Albion fightback at Gresty Road.
Goals either side of the break from Danny Shelley and Ashley Westwood put Crewe in the driving seat before Callum Driver pulled one back for the visitors. Murphy put Crewe two up again before Calvin Zola netted in injury time for Albion.
"It was harsh that we didn't get the win, let alone the draw," said Peschisolido.
"They had four chances and scored three of them and our keeper had to make a great save for the other, while we missed a lot of chances.
"We defended poorly for the first goal. We had worked all week on staying with the runners but then we didn't do it when it mattered. The belief is still there for us and we are staying positive."