Kim Bo-Kyung netted a last-gasp equaliser for the Welsh club as they came from behind twice to salvage a point at the Cardiff City Stadium.
And Nigeria striker Odemwingie revealed the result gave him a sense of "belonging" in the English top flight.
"Belonging in the Premier League was the first thing that came into my mind when we equalised," he told Wales Online.
"The joy around the stadium, I felt like Cardiff is here to stay. There is a lot of work to be done and confidence is the key.
"This is the first year in the league but the performance we showed we are not like the struggling sides. Sometimes we don’t show the best football but the spirit of the team is very strong.
"I have been in situations where everyone improves and you become a very solid side in the Premier League."
Cardiff currently sit 15th in the Premier League, three points clear of the relegation zone.
