City have been scoring freely throughout the season, but they drew a blank at Carrow Road in the Premier League on Saturday as the Canaries claimed a vital point in their battle against relegation.
"It was a good point to take," said their Sweden full-back Olsson. "They are one of the better teams and we worked hard today so it felt good.
"We've been working hard in training, mostly defensively and it paid off today at least and we've just got to keep working on it and hopefully we'll keep more clean sheets."
Fellow defender Joseph Yobo was handed his Norwich debut after being signed on loan from Fenerbahce, and Olsson was impressed with how the Nigerian handled the pace on his return to the Premier League.
"I don't think it was such a big difference for him," Olsson added. "He's got experience as well. He played at a big club in Turkey so it wasn't a huge difference for him I think and he's been doing well in training so I think he fitted in well.
"I think City made it difficult for us but we frustrated them as well. We were disciplined and we sat back with the midfield as well so I think we made it hard for them today but they are a good team and we are just happy with a point.
"It's tight (at the bottom) but I don't think we can really think about the other teams. We've just got to go out there and play our football and start picking points up.
"We're just working hard in training and hopefully we'll get enough points to get away from the teams round us at the bottom.
"We're keeping clean sheets but the most important thing as well is scoring. Hopefully that will start to come soon.
"The strikers will hopefully start scoring soon but we've just got to work together as a team. Sometimes you don't score but you never know when that might change."