It was a 42nd career hat-trick for Messi, 38 of which have come for Barcelona, and his boss could not help but sing his praises following the Camp Nou rout.
"I am happy for Leo who scored three goals and is extraordinary," Valverde said at a post-match press conference. "We pulled through a complicated game, because these kinds of matches are always tough.
"Despite the result, it wasn't easy. Espanyol fought very well, but we have great players like Messi, who scored three goals, and Suarez, who gave everything like the rest of the team."
The result puts Barcelona, who host Juventus in the Champions League on Tuesday night, two points clear at the top of the table, having yet to concede a goal in their three La Liga victories.