Cousins captained the Redskins' offense for the final 20 minutes of the game, leading them on a 78-yard touchdown drive and earning a 92.7 passer rating for the game.
Unfortunately, his debut unraveled with a pair of interceptions with less than two minutes remaining, cutting short any opportunity for a comeback victory.
After the game, Cousins chalked both picks up to trying to do too much.
"The second one, I was just trying to do too much. I was trying to get it all back on one play."
"It was tough," he said. "I thought he did a great job in that third down and 10-plus. Made the right key, got us going at the end of the game."
Shanahan said that Griffin III was diagnosed with a mild concussion during the game and could not tell medical officials the quarter or score. It is yet unclear if he will be available to start next Sunday's game against the Vikings.
If he is not, Shanahan has confidence in Cousins's development at quarterback.
"[Cousins] has grown in experience and I've got a lot of confidence in Kirk," Shanahan said. "We'll see where it leads us."
Despite a disappointing end to his NFL debut, Cousins classified today as a positive learning experience on the whole.
"It wasn’t the result that I wanted in the end, but there were good things I can take away from it," he said. "There are other things I need to learn from and I will certainly do that."
Cousins credited his teammates for continuing to fight when he came in the game, never losing confidence in the Redskins ability to win.
"I thought I received a lot of support from my team. We always have a sense of belief," he said. "We’re a tight-knit group and we’re playing for one another out there.
"The result at the end of the game wasn’t the one we wanted, but these guys are going to stand by me, they’re going to stand by Robert, so we’re moving forward."