The treble winners occupied two of the three podium spots in Zurich, with Messi winning his fifth prize by a wide margin ahead of Real Madrid's Cristiano Ronaldo.
Neymar took third place, a new personal best for the Brazilian - but his compatriot believed his 2015 performances merited an even better spot.
"Yes, it surprised me [that he did not finish second], but everyone starts crying when I say these things and speak my mind," the right-back fired after the ceremony to AS.
"Neymar has gone through an incredible evolution and he’s a better player every day, of course he’ll keep competing for the award, he wants it and will work to win it."
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Alves did point out, however, that until Messi relented he found it hard to imagine a different winner in the coming years.
"[He can keep winning] for as long as he wants. If he keeps going like he is now he won’t have any competition," he said.
"The years pass and he just gets better. We’re privileged to have him with us."
Messi, Neymar and Alves were all picked to the FIFPro World XI for 2015, with Andres Iniesta completing the Barcelona quartet.