The Spain international finished third in the poll for the third straight year as Messi picked up the award, while Real Madrid's Cristiano Ronaldo came second.
Upon receiving the prize, Messi paid tribute to Xavi, saying it was "a pleasure" to play alongside the 31-year-old.
"Of course, it [Messi's words] moved me, I liked it a lot," Xavi told Esport3. "It is better than winning an award.
"I did not expect him to thank me, he is a great friend of mine and an amazing person, but he is shy."
Uefa president Michel Platini was coy when asked if Messi could become the best player in football history, but Xavi believes there are no limits to the Argentine's potential.
"It is true that if he continues at this level, he will be the best player ever," Xavi added. "I have no doubt about it.
"He is the one who has to test his own limits. If he continues like this, he will break all records.
"I am happy for him, because he is my friend and also a great guy."
Meanwhile, Andres Iniesta said that Messi is a worthy winner of the Fifa prize, enthusing: "He is a unique player and therefore he deserves to win the Ballon d'Or, just like Xavi does.
"I am happy with it because he is a great team-mate. It is good to be playing with such team-mates.
"[Pep] Guardiola also deserves his award because those who know him know how hard he works.
"The important thing is to keep working. For us there is nothing better."
Starting in November and continuing through January, Goal.com is publishing exclusive extracts from Graham Hunter's highly-anticipated new book, 'Barca: The Making of the Greatest Team in the World'. Last Friday's extract took a closer look at the most influential figure in the club's history: Johan Cruyff: Don't miss it!