Players continually slipped on the surface and chunks of turf came loose at regular intervals as the Serie A side frustrated the holders ahead of Tuesday's return leg at the Nou Camp.
"[Barcelona] passed the matter over to UEFA delegate Mikalai Varabyov at the post-match meeting," the Spanish team said in a statement on Thursday.
"Varabyov has included the complaint in his report and UEFA will demand an explanation from the Italian club.
"In the end we adapt to everything ... but it's clear that this was a problem for the spectacle," said Barca coach Pep Guardiola in his post-game news conference.
AC Milan vice-president Adriano Galliani acknowledged the pitch needed resurfacing and said they were in talks with Inter Milan, the club they share the stadium with, to find a solution.
"At the end of the season if we have an agreement it can be done," Galliani told the Italian sports daily La Gazzetta dello Sport. "I'll fight for this new pitch."
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