The Chiefs took a 13-0 lead early in the second quarter, with the Browns finally getting themselves on the scoreboard with just 2:44 left of the first half when Josh Gordon got on the end of Jason Campbell's 39-yard pass.
Both sides struggled for points in the second half, with Cleveland outscoring the Chiefs 7-3, leaving Chudzinski bemoaning their scoreless first quarter.
"We weren't able to make the plays at the end there to win the game. Kansas City started fast and we weren't able to get anything going early in the game," Chudzinski told the Associated Press.
"I thought our guys did a great job of fighting and getting back in the game. We were in position a couple of times, one break or one play."
The result leaves the Browns third in the AFC North, while the Chiefs remain unbeaten this season with a perfect 8-0 record.