"[Messi] has a small problem", Valverde said.
Without a win in their first three Uefa Champions League ties, they did not win any of their opening six league games and were 15th as recently as December.
Valencia took the lead in the 24th minute, however, when a quick counter-attack ended with Rodrigo Moreno feeding Gameiro and the Frenchman expertly found the bottom corner of the net. "I don't know too much more".
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Approaching a key stretch in the season, with crunch Copa del Rey and Champions League matches to come and the title race a long way from over, Valverde's decision to leave Clenment Lenglet and Jordi Alba always looked a risky one.
Barca's captain helped his side with a 38th-minute penalty that beat the outstanding Neto.
The league leaders rallied and Messi scored either side of half-time to clinch a point in a match packed with incident.
But this Clasico may be without both Messi and Cristiano Ronaldo - who was sold to Juventus in the summer.
Valencia's goalkeeper was also forced to tip over Sergi Roberto's cross which was destined for Luis Suarez at the far post but, just as the hosts were starting to build some pressure, they fell victim to a sucker punch.
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That includes what he described as his " Spartacus moment " during Brett Kavanaugh's Supreme Court confirmation hearings last fall.
But Messi appeared to suffer with a thigh issue in the second half, receiving treatment on the touchline before returning to the action as Valencia held on.
Arturo Vidal flicked the ball to Messi, who took one touch to set himself up before unleashing an effort beyond Neto in the Valencia goal.
But Atletico Madrid, now six points behind, can close the gap when they take on Real Betis on Sunday.
Barcelona might have levelled in the 44th minute when Roberto struck a powerful attempt towards the bottom corner, but the post came to Valencia's rescue, before Messi volleyed an Ivan Rakitic pass over the crossbar in the final action of what was an incredible first half of football in Catalonia.
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