The Scottish side marched to the semi-finals of last season's tournament but have failed to win a single match in this campaign.
They headed into the Stade Yves du Manoir clash on the back of heavy reverses to Saracens and Munster, in which they did not put a single point on the board.
Greig Laidlaw slotted three penalties to break their scoring duck, but it was not enough as tries for Racing from Juan Imhoff and Ben Arous proved the difference.
Bradley was pleased with his players' commitment, but was left frustrated at their failure to turn prolonged pressure into points.
He said: "We're disappointed with the result because we came here to win and we didn't.
"We haven't performed to the levels and standards we set ourselves in the first two games of this Heineken Cup season but this was totally different and we were in the game right to the last minute.
"The boys played well and the frustrating thing is that we had opportunities throughout the game. The period at the start of the second half saw us dominate the game and I felt that if we could have scored then, the game would have swung our way.
"But to give Racing their credit, they produced a strong defensive show in that 20-minute period to hold us out, which was a crucial part of the match.
"Unfortunately they then scored a try with probably their only real shot at our line in the second half and that was it. On another day, it could all have been very different."
Edinburgh, who remained rooted to the bottom of Pool One, welcome the Parisians to Murrayfield next Friday.
The Scottish outfit could be without Tom Brown, who suffered a knee injury, but Bradley has urged his side to build on their positive display.
He added: "Despite what happened in previous weeks, we did not come here with the attitude just to limit what Racing could do with the players they have.
"We came here to win but we will take the positives from the attitude the players showed and we are looking to beat them next week at Murrayfield."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.