Odemwingie, Albion's top scorer with 15 goals last season, is hoping the derby win will kickstart his and the club's season.
He said: "I could feel the importance of this game from the first day I arrived back from the national team, with the way the fans were talking about it.
"I knew it was a big game so when I scored the goal I felt double joy.
"We climbed up the table and it was an important three points and to get the first home victory of the season is great. Now we all want to kick on from here."
Odemwingie added: "With the goal I didn't have time to think. It was like a training situation. I saw the goal and just relied on my instincts.
"I'm glad it went in and we climbed up the table and I scored my goal, so everything is good."