The draw presented Atletico Madrid, playing on Sunday, the chance to close the gap at the top to three points.
Valencia, who hit the woodwork in the second minute, went ahead in the 24th with a well-taken finish from French forward Kevin Gameiro and doubled their lead with a powerful penalty from Dani Parejo in the 32nd.
"[Messi] has a small problem", Valverde said.
We will wait to see what the doctors tell us when they do the tests and we will look at it.
Messi also has 10 assists for Barcelona on the season.
Los Che almost stunned the hosts after Daniel Parejo forced Marc Andre Ter Stegen to a low save, with the rebound shot from Denis Cheryshev hitting the face of the post.
Messi took his tally to 11 in the last nine matches in all competitions, passing 20 league goals for the 11th successive season.
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The Galaxy S10 family is also reportedly in mass production - just weeks ahead of the formal launch that is set for February 20. It's also worth pointing out the S10E will only ship with two rear cameras instead of three like on the other two S10s.
Little did it matter that the team's all-time leading scorer had just struck two goals to lead Barcelona back from a two-goal deficit to secure a 2-2 draw.
More preventable still was Valencia's second goal, with Sergi Roberto out of position at left-back and out of position in the moment too, shoving over Daniel Wass to stop him reaching a cross.
Valencia were weakened when Gameiro departed injured after 40 minutes.
Okay Yokuslu scored 17 minutes from time to give the hosts a much-needed victory, only their sixth of the season, to end a five-match losing streak. "If he's in good shape, he'll play on Wednesday".
Fourth-placed Sevilla have won only one of their past six league games.
Neto made a terrific save to keep out a curling Messi effort early in the second period, before Luis Suarez had a goal-bound shot blocked in the 49th minute during a period of intense pressure from the home side.
Real Sociedad defeated Athletic Bilbao 2-1 to deal its northern Basque Country rival its first defeat since the arrival of coach Gaizka Garitano.