Viviane Reding, an MEP, scolded the Prime Minister for "playing the man and not the ball" in his opposition to Mr Juncker's presidency bid.
Ms Reding, also a Luxembourger, urged the PM not to nominate a Eurosceptic as Britain's European Commissioner and said there was a "good argument" for sending a strong woman.
Reports suggest early frontrunner Andrew Lansley has fallen out of favour, with Eurosceptic former Tory leader Lord Howard being mentioned in dispatches.
Ms Reding said: "I think the whole Luxembourgian country and all its population was offended because that was clearly playing the man and not playing the ball and we did not appreciate all the negative sounds which came out of Great Britain."
Ms Reding urged Mr Cameron to send a woman rather than a Eurosceptic to Brussels.
She said: "(Sending a woman) certainly would help because there are not enough women candidates and no government, no European government, can be built in this type of world without enough female talent on board."