He spoke as opinion on the continent against his opposition to the candidacy of veteran federalist Jean-Claude Juncker hardened.
On the campaign trail in the Newark by-election, the Prime Minister was asked why he was against the former premier of Luxembourg, whom "nobody has ever heard of".
He replied: "We need people running these organisations, whether it's the European Council, the European Commission or indeed any other part of Europe...that understand an open, flexible, competitive Europe that respects nation states and realises that the process of getting too big, too bossy, too interfering has gone too far and needs to be rolled back .
"So that's what matters when it comes to these people, as you say, that no one has ever heard of. We need people that get it. That is my clear instruction on this and I look forward to the continued debate in Europe."
Earlier No 10 highlighted a point made by Angela Merkel, the German Chancellor, last week that there can be "no sense of automaticity" when it comes to appointing the person to succeed Jose Manuel Barroso at the Commission.
However, since expressing coolness about Mr Juncker's candidacy last week after an informal Brussels summit, Mrs Merkel, after facing pressure at home, has come out strongly in favour of the former Luxembourg Prime Minister.
Elsewhere, Tony Blair said the role of the Commission presidency should go to "the best person" but indicated it should be a reformer.
In a speech at the London Business School, the former PM set out an agenda for change in Europe, warning it would be "complacent and dangerous" to ignore the rise of eurosceptics. He argued Britain must lead reform rather than sever ties with Brussels. "People can understand that immigration may be a good thing but they want some rules and order about it."