The NFC East champions ended the season with seven straight wins to make the post-season for the first time since 2007.
The backup quarterback told the team's website: "We have a lot to be proud of and remembering this feeling going into the off-season, I think, will strengthen us as a team and bring us together when we go into our preparation in the spring.
"There is only one team happy at the end of the season. There are 31 teams that feel like this at some point. It has been a great year to win seven in a row and pull ourselves out from where we were."
Cousins made one start for the Redskins during the 2012 regular season while Robert Griffin III dealt with a knee injury.
The Redskins lost in the wildcard round of the playoffs to the Seattle Seahawks.