Barcelona were held to a draw at the Mestalla with Jordi Alba cancelling out Rodrigo’s early strike.
However, the game was marred by a controversial incident involving Messi, with the Argentina international seeing a goal wrongly disallowed with the officials failing to notice his ball had considerably crossed the line.
Valverde refused to be too critical after the game, praising Barcelona for the grit and determination showed against their fellow title rivals.
But Spanish outlet Diario Gol say Valverde’s decision not to force the issue has rankled with Messi.
For years, Barcelona and Real Madrid have traded verbal blows.
Media outlets in the region have accused both sides of receiving special treatment from the officials – despite there being little evidence of such.
And Messi supposedly feels Barcelona purposely were cost a vital three points against Valencia.
Diario Gol say Messi made his feelings clear to Valverde after the game.
He supposedly berated the manager, believing him not be interested in defending the interests of the club.
Other heavyweights – though unnamed – reportedly got involved.
However, Valverde has since upped the ante by criticising the decision, labelling it as “absurd”
“What is absurd is that people in the top row of the stadium can see that the ball is in and those below them can’t,” he said in a news conference.
“From the assistant’s view, he couldn’t see it,” he said before tonight’s Copa del Rey clash with Real Murcia.
“I couldn’t, either. But from the moment I saw what happened, I knew it was in because of how Leo celebrated, how the goalkeeper had his head down… [Martin] Montoya went to get the ball to take it back to the middle of the pitch.
“It’s crazy that in such an important game, and at an important moment, the referee doesn’t see it when there are 40,000 people that knew it was a goal.
“Every year there’s an episode like this. Last season it happened to Barca at Real Betis.”