The Seahawks struggled on offense for the whole game, with quarterback Russell Wilson being sacked seven times while making just seven first downs and 135 yards.
However, their defense held firm to help them to a 14-9 win, and Carroll acknowledged that his side were lucky to pick up the victory.
"We were very fortunate. Under the circumstances with a new quarterback, they did a great job," Carroll told The AP.
"We just couldn't get going on offense. Fortunately, the defence hung together and gave us a chance to win the game."
The result ensures that the Seahawks remain top of the NFC West, while the Rams drop to the bottom of the division.