Neco Williams had Forest ahead on two minutes before they were pegged back on 20 minutes by Jaidon Anthony.
Parker said afterwards: "The point is fair enough. Over the course of the game we had some good chances, Forest had some as well. A point is a fair result.
"Not ideal. To come out that early and for them to get in front wasn't ideal. hat pleased me most was our character. We came with a real dominance after that.
"I'm learning things about the team, what is being confirmed is this team have got some real character. When they need to dig in they dig in. This was our best performance in terms of showing our character. We keep improving."
On Luis Florentino's performance, Parker said: "His experience, his calmness, the boy has been on this stage and you see that in his quality today, certainly after an early booking."
He continued: "Kyle (Walker) was every bit of the player that we expected to come in today. A driving force for us. At the end, he was on fumes and there is something in him that he has to push. I'm always reluctant to single out individuals but him and Martin (Dubravka) were very good.
"There's no denying this year, the quality we are up against the goalkeeper is going to play a pivotal role. He was vital for us. We knew that when we brought Martin in."