"I got terribly nervous about this," said the broadcaster, who rode with Princess Anne when the pair were both amateur jockeys. "I've been pretty busy then suddenly yesterday I thought 'gosh I'd better make sure everything's in order for tomorrow'.
"I'm still a bit shaky now," added Clare. "I talked absolute gibberish, absolute gibberish - I was just hopeless.
"I mucked my curtsey up, nearly fell over as I turned and walked away, messed up properly, but luckily not too many people had seen that."
Hampshire-born Clare has been awarded for 18 years of service to both radio and television including her coverage of London's 2012 Olympics, the Paralympics and the Queen's favourite Royal Ascot.
The 42-year-old has presented numerous horseracing events and hosted Countryfile, Crufts and BBC Sports Personality of the Year.
Clare was joined by her partner Alice Arnold for the investiture which also honoured Dragon's Den star Hilary Devey.
"This is an incredible personal moment and it's lovely to have this recognition," said Clare. "But I feel the job that I do, I get so much satisfaction from it and I enjoy it so much and I want to keep challenging myself and try to make myself a better broadcaster."