Messi converted a penalty in the first-half before scoring a second-half hat-trick, while for the second straight match Denis Suarez and Paulinho each found the back of the net in what was a straightforward win for the hosts.
"Eibar are a brave team," Valverde said at his post-match press conference.
"If you look at the score after the game, it seems we've won easily but that wasn't the case.
"They often put us in a tight spot."
Paulinho scored for the second game running and already appears to be changing the minds of many supporters.
"He has a strategy to arrive in the area," Valverde continued.
With four goals, Lionel Messi was a clear man of the match.
"He is the most intelligent player that I have ever seen on a football pitch," the coach enthused.
"You don't know how, but he just appears."