Lewandowski was widely expected to win the award last year but it was cancelled because of the Coronavirus pandemic.
The Poland international finished second behind Messi when this year's awards were organized on Monday.
Messi, who joined PSG on a free transfer in the summer, won the Copa del Rey with Barcelona last season and was top scorer in the Spanish top flight, while he finally ended his international trophy hoodoo by captaining Argentina to Copa America triumph.
Lewandowski scored 41 Bundesliga goals in 29 games last season and helped Bayern Munich win the FIFA Club World Cup and German top flight.
"From a Bavarian, Polish and also from a German point of view, the presentation of the Ballon d'Or yesterday evening was definitely a disappointment," Muller wrote in a post on his official LinkedIn profile.
"For some even a little more. Although I've been in the business for a bit longer and was therefore not really surprised at the outcome (it was similar with Franck Ribery in 2013), the whole thing formed or reinforced a thought in me: We have great players in the Bundesliga and we have to not hide us. However, further international successes are necessary for global recognition.
"This is also a huge motivation for me to put everything into the balance in order to bring the Champions League back to Munich and to show the football world what is going on. And above all, what German football has to offer.
"We have the next opportunity to do so next Wednesday in the Champions League game against Barcelona. Let's tackle it!
"PS: With Lionel Messi, he is probably the best individualist football has ever produced. So congratulations to Lionel on winning the Ballon d'Or, even if I think that Robert Lewandowski would have deserved it more this time."
