The centre will not be returning to the Ravens in 2013, having announced his retirement after 15 seasons in the NFL.
The 36-year-old told Sports Illustrated: "I will miss playing with Joe. Special guy. I really admire him, how he goes about his business.
"He doesn't get full of himself, doesn't buy into the hype, doesn't make the game too big. I wish I was that level-headed."
Birk moved to the Ravens in 2009, the season after the franchise drafted Flacco.