"We always dwell on the positives at this club" said Rodgers.
"The players don't dwell on that long run without a home win because it can change in a moment. A bit of luck can lead to
one win and then you can go straight off on a winning run.
"The crowd can see what we are doing and we are not far away. I am trying to give a new identity to the group and asking them to show courage and pass the ball.
"We played some wonderful football but we need to be killers in the penalty area. We can dominate possession and we are only a matter of inches away from being very, very good."
Jubilant Cardiff manager Dave Jones was relieved with the win after two successive defeats.
"It's a difficult place to come and to get three points and it means I can drive home with the chairman in a good mood," he said.
Jones is likely to appeal against Stephen McPhail's second-half dismissal for a foul on Jem Karacan.
"It looked a little bit harsh although his foot was up. After that we had to reorganise and play dirty football.
"I thought our goalkeeper and two centre-backs were magnificent after we went down to 10 men."
The only goal came from Chris Burke, his first of the season, after 58 minutes. From eight yards out his right foot shot went high into the Reading net after he collected a left-wing pass from Peter Whittingham.'
When these sides met last season Reading grabbed an injury-time equaliser through goalkeeper Adam Federici who went up into the Cardiff penalty area.
They almost repeated the trick during the five minutes of added time at the end of this game.
Federici again went up for a corner and tried a spectacular overhead scissors kick which was comfortably saved by Cardiff's David Marshall.
"If that had gone in I would have sacked the lot of them" joked Jones.
"He told me he was aiming for the top corner," said Rodgers.
Cardiff should have made the game safe during a spell of first-half dominance in which Jay Bothroyd in particular spurned a number of chances.
By contrast Reading's best chance came in the first minute when Noel Hunt saw his close-range shot saved by Marshall.
Reading were at their best early in the second half when but a lack of firepower is clearly their biggest problem with Simon Church's low drive their best effort - until Federici stepped up in the dying seconds.