Moyes was delighted with the way the support backed them on the day as they lost 2-0.
He remarked afterwards: "I think they recognised the efforts the players put in. In some ways, it might have been one of our best performances away from home, but we couldn't score the goal and we just dropped a couple of runners at times for their goals.
"We had bits of the game but we didn’t take the chances from it. So, look, it’s generally an improvement on where we've been. But obviously, we want improvement and the results of the game.
"I didn't think we played great against Nottingham Forest, but we won 3-0 last week. I thought we actually played better today and lost 2-0. So, I'd rather take that the 3-0 win rather than today."
Moyes also said of the sold-out away section at the Bridge, "The players knew they could walk to our fans at the end because of how well they performed and the supporters knew how well the players performed.
"You couldn't leave today because we were right in the game right to the end, even up to the last minutes we were trying to score. Unfortunately, we couldn't get back in it."