Midfielder skippers Canaries in London
A resilient defensive display kept the Blues at bay for long periods, while home goalkeeper Asmir Begovic was also called into action several times across the course of the 90 minutes.
However, Alex Neil's men were ultimately undone by Diego Costa's 64th minute strike, and after the game O'Neil told Norwich City TV: "It's a strange one because we've worked so hard, which gives us a sense of pride.
"We had a real go of it, and we're leaving disappointed because of the manner of their goal. Our defensive shape was good and we've carried out our game-plan well, only to switch off at a quick free-kick.
"Everyone knew it was going to be tough test, regardless of where Chelsea are in the league. To be punished how we have been is disappointing at this level."
O'Neil, who captained City in the absence of Russ Martin and Alex Tettey, is now determined to quickly switch attention to next weekend's game against Arsenal at Carrow Road.
"Although we're disappointed, it's important to focus on going again now," the 32-year-old added.
"It's not going to be easy, but the good thing is we're at home. We'll be able to press slightly higher and have slightly more of a go than we have on the road.
"We didn't go toe-to-toe with Chelsea, as that was never our plan. We knew we'd have to sacrifice their half of the pitch to protect ours while trying to counter when we had the opportunity.
"On another day Seb Bassong's chance in the first half goes in, and from then on who knows? Everyone has to play these teams, so it's about doing your best to collect as many points as possible."