The Robins held their own against the might of the Premier League outfit but essentially saw a flat-footed backline caught out by two clinical attacks in the first half, allowing Fernando Torres and Ramires to score.
The League One hosts could be proud of their display and enjoyed a couple of chances of their own, Dany N'Guessan correctly ruled marginally offside with a second-half header, cutting short the celebrations of most of those inside a sold-out County Ground.
But Cooper was left to rue the fact his side did not pose a greater threat going forward.
"I was pleased with our possession but just a bit disappointed we haven't really tested Chelsea enough," he said.
"Second half we had a lot of possession, we had a couple of good headers, one of them disallowed, and it would have been interesting if one had gone in.
"I was just a bit frustrated we didn't create more than we did going forward but we have to remember who we're playing against.
"It would have been nice to get a goal and ask a few more questions towards the end but to do that against Chelsea you really have to be on top form.
"But fair play to the players, they applied themselves very well, their attitude was good and they passed the ball really well at times again."