Messi gave his side the lead with an exquisite free-kick, but West Ham flop Calleri equalized from the spot for the relegation battlers.
"We felt that they equalised with an "invisible" penalty, they grew stronger after that and we played in too much of a hurry", the agitated Valverde said.
"We didn't understand it at the time it happened, it was inexplicable".
"We lacked a bit of precision with the final ball, with the final decision". It did us a lot of damage - for how it was given and the sensation it left us with.
Both would have seemed harsh and Valverde was furious with referee Antonio Mateu, particularly after goalkeeper Leandro Chichizola had gone unpunished on the stroke of half-time when he appeared to deliberately handle after rushing out of his box.More news: Could Northampton's Prezzo be at risk?
He said: "I want to make the most of this great football moment and help the fans enjoy themselves".
"Las Palmas defended well, we tried to break them down but as the game progressed there was less rhythm and it got more and more hard". "It was a clear handball outside the area and he's not seen it".
Antoine Griezmann delivered a resounding message to Barcelona by scoring four goals against Leganes in La Liga ahead of Atletico Madrid's crunch match at the Nou Camp on Sunday.
Less than a month ago, Valverde's side were 11 points clear at the top but their advantage could be cut to just two points if they lose this weekend's top-of-the-table clash. We go into it with a bad taste in our mouths, because we could have got a win.
Griezmann added his 101st Atletico Madrid goal before the interval, smashing home a 25-yard free-kick to put his side on track for an eighth straight league win, and tacked on two more in the second half to run his personal total to 103 for the club.
"I've always said a referee has a hard job but in the first half we clearly saw their goalkeeper commit a handball so the draw leaves us with a bitter taste", Iniesta told reporters.