The on-loan Chelsea midfielder struck the equaliser for the 1-1 draw - his first in a Saints shirt.
"It wasn't an easy year for them (the fans)," Ugochukwu, who celebrated by running to the fans and pointing to the badge on his shirt, told the Daily Echo. "I just want to say thank you to the Southampton fans.
"They've been with me, even if it wasn't easy. Even if the team were battling. I said thank you because the support is just huge. That's my way to just say thanks.
"I'm very happy because I think we deserve it. We had a good game. It wasn't easy, especially when it's not at home.
"I'm very happy for the guys because we fought very hard and we deserve it. We felt a goal was coming because we were pushing.
"I think the boys who came in as well helped us. It's very good to have players who are coming on the pitch and giving their best. I think it's a very good point."
Southampton experience good for me
Of his time with relegated Saints, Ugochukwu remained positive.
He also said, "We will come into the next game against Fulham. Then we'll do our best to get more points. Then we'll see.
"I think as a young player, it's a very good experience at Southampton. I think in hard times, you learn a lot.
"At the beginning of the season, I wasn't playing really much. Now we're back in the Championship.
"I think it's a very good experience because mentally, it made me grow a lot. Now I know what it takes to be in the Premier League. Let's keep fighting."