The loss was the seventh in a row for the Browns, who finished the season with a 4-12 record overall, worst in the AFC North.
Chudzinski's first and only year with the Browns was a rocky one, as the team faced injuries to both the starting and backup quarterbacks and never found consistency.
Cleveland also traded their 2012 first-round draft choice (third overall) running back Trent Richardson just two games into the season.
"We appreciate Chud's passion for the Browns, and we have great respect for him both personally and professionally," the Browns said in a statement.
"We needed to see progress with this football team. We needed to see development and improvement as the season evolved and, unfortunately, we took a concerning step backward in the second half of the year."