TV replays showed minimal contact between the pair and Davies, renowned for his physicality, feels his reputation went before him.
The 32-year-old has had issues with Clattenburg before and has been booked by the official four times this season alone.
"It was a clear goal for me," said Davies. "Having watched it again, the referee said I put two hands in his back - but I can't see it.
"I think he [Hangeland] got under the ball and I just outjumped him.
"His reaction - he hit the floor and he knew it was a fair goal.
"When I saw who was the referee I didn't expect to get anything off him. Over the years I have never got much from him.
"There was a penalty at Old Trafford last season and he did nothing - but I got a booking.
"Numerous bookings over the years - I don't know, I have always felt there is something personal there.
"Every time he referees us, I don't expect to get anything.
"At least I didn't get a booking. That was the only good thing about it."
Davies and Clattenburg were two of the central figures in an infamous clash between Bolton and Manchester United in November 2007.
Davies was booked on that occasion but Sir Alex Ferguson felt he should have been sent off after a number of challenges on Patrice Evra.
The United boss was even sent to the stand by Clattenburg for his protestations during the game.
Clattenburg's latest brush with Davies left Bolton having to settle for a goalless draw that left them one point above the relegation zone.
Davies added: "We weren't at our best but they didn't cause us any problems.
"Johan [Elmander] had a great chance and my header should have taken all three points.
"This game has gone, we got a clean sheet and took a point - but it was a game we thought we should have won."
Man. City 2/5, Draw 10/3, Bolton 8/1