Wood struck in a game that saw three red cards. Forest boss Nuno and Brighton counterpart Fabian Hurzeler both saw red after Morgan Gibbs-White was sent off for a tackle on Seagulls striker Joao Pedro.
Wood later said: "It is always good to get something out of the game when coming away from home in the Premier League. Brighton is a tough place to come, they are a good side.
"In the manner of how the game has played out, at times we deserved the point, but we had to work hard for the point as well."
On the three red cards, he continued: "I would have to see the challenge back, I have not seen it. It is one of those, Morgan has made a rash decision and we have to move on with that. The managers will have to come and comment on that, that is what they do.
"Everyone wants to win and fight in the Premier League and points are hard to come by."
On failing to capitalise on the lead, Wood added: "We got into the lead well and they weren't causing us too much problems until the goal went in. Then we went on a down spell and they had a good spell, they are a good side, and that's how it goes.
"Unfortunately we couldn't capitalise on it, but we have a strong character in the group, fought back and scored a lovely goal to equalise."