Back-to-back draws against Espanyol and Getafe had left the door slightly ajar in the title race and Luis Suarez's opening goal came despite a tide of relentless pressure from Jose Luis Mendilibar's hosts during the opening stages.
Eibar were barely discouraged by Fabian Orellana's red card midway through the second half and Barca needed Jordi Alba's goal two minutes from time to make sure of extending their lead at the top over Atletico Madrid to 10 points .
"Our objective was to win after back-to-back draws," Valverde told a post-match news conference.
"Eibar have a way of playing which demands you play in a certain way.
"Each time we got past that first line of pressure, we could have scored because they were taking lots of risks.
"Everyone suffers at Ipurua, no one wins here easily. Even Atletico only won in the last minute."
"Tuesday's game is another story. We will try to produce a good performance," said Valverde, who credited Eibar for providing ideal preparation ahead of facing Antonio Conte's Premier League champions.
"Today was a good test before Tuesday. We had to suffer a lot, Eibar are in good form and it was a really difficult game.
"Hopefully that will benefit us going into the midweek game, even though it's a different competition. Eibar pressed us a lot. They were very good."