Olsson spoke out in support of Odemwingie, who was subjected to racist jibes during his spell at Lokomotiv Moscow.
Albion fans funded a banner saying 'Thanks Lokomotiv' in response to a slogan displayed at a recent Moscow game, which said 'Thanks West Brom' and included a banana.
Olsson said: "We heard about the stick he got at Lokomotiv and credit to our fans for such great response.
"It's still part of some stadiums and society in general.
"It's the 21st century and I can't believe we still have these issues.
"It's very sad but I don't see it as a big problem at English football grounds - and that's nice of course.
"Peter is a great player. His engine is massive and he keeps running for 90 minutes. He's already put two goals in and hopefully he'll keep doing that.
"He's a very nice guy and he's settled well into the team.
"He speaks very good English, which helps as well.
"We are all glad he was a matchwinner for us on Saturday."