The boot of Gareth Steenson eventually settled the game late on to ensure Blues finish runners-up in Pool 2 on 14 points and have an anxious wait to see if results fall their way to claim a quarter-final spot in the Amlin Challenge Cup.
"We are massively disappointed by the result, but all of the coaches are very proud of the way the players fought back," said Davies.
"Exeter started like a train, to be fair to them, and were excellent. But slowly and surely we crept back into the game and went in at half-time 13-10 down.
"We continued in that vein after the break and had good field position and got into the right areas of the field. But we didn't quite take the opportunities when we were down there which is a shame.
"We just lacked that control and at a couple of key moments in the second half they got penalties and just snuck the win. Credit to them, but I was pleased with the way we fought back.
Davies also praised the way his youthful side showed a real maturity in adversity adding: "We had a young team out there and they got stuck in. It's just disappointing not to win and keep a clean sheet at home in Europe this season.
"Since the autumn we have made progress, the most we have since I have been here. The players have been fantastic the way they have cracked on.
"We haven't always had the results but everyone can see we are getting better. To be in with a shout of the Amlin Challenge Cup quarter-finals is great.
"I thought Ellis Jenkins was excellent today and people like him and Kristian Dacey are growing. I don't like to single them out but they are getting better all the time."