Real Madrid's Croatia midfielder Luka Modric took the prize on Monday in Paris after winning the Champions League and being named player of the tournament at the 2018 World Cup in Russia.
The 33-year-old's triumph ended Messi's and Cristiano Ronaldo's decade-long reign, with Juventus's Portugal striker finishing second and Messi fifth in a vote by 180 journalists.
"I will not get into discussing the inconsistencies of the prize," Valverde told reporters.
"We congratulate Modric for winning the Ballon d'Or but Messi being in fifth place is absurd."
Messi, a five-time Ballon d'Or winner, led Barca to a La Liga-Copa del Rey double last season but Argentina went out of the World Cup in the last 16 to eventual champions France.
The Barca No. 10 also won a record fifth European Golden Shoe after finishing with 34 top-flight goals last season.
Modric got 753 points followed by Ronaldo on 476, Atletico Madrid's Antoine Griezmann with 414 and Paris St-Germain's Kylian Mbappe was fourth with 347, ahead of Messi on 280.
Barcelona host Cultural Leonesa on Wednesday in the second leg of their Copa del Rey round of 32 tie, in which they hold a 1-0 advantage, although Messi is not expected to feature.
(Reporting by Rik Sharma; Editing by Ken Ferris)
