Defeat saw Forest equal a club record of seven games without a goal to remain third bottom, in contrast to their visitors who are fourth in the table.
But while Forest were left searching for their first goal in 10-and-a-half hours of football, Scotland striker Kenny Miller supplied the finishing class that separated the sides.
It was tough on Cotterill's team, who did everything but score in a battling performance that brought praise from both managers.
Cotterill could not believe his side emerged from the game with nothing to show although he admitted they are not helping their own cause by failing to convert the chances they are creating.
He said: "We have had treble their number of shots and lost the game 1-0. It's difficult to take.
"There's not a lot wrong with us but we are putting ourselves under immense pressure by not taking the chances that come along.
"Once more I am saying we didn't deserve to lose but that was certainly the case today. I thought we were the better team but things are just not going for us.
"I don't think I have experienced a run like this but we will get ready to go again at Ipswich on Monday and try our best to make things happen for us.
"We have to do that because there is no other way. We will go on searching for a solution because there is no fairy godmother who is going to give us it on a plate."
Cardiff boss Malky Mackay believes Forest will get out of their predicament if they continue to play as they did today.
He said: "If Forest keep playing like that they won't have any problems. I've never had an easy game against Forest or against Steve Cotterill and I certainly didn't have one today.
"We toughed it out and that pleased me enormously because we had to work really hard and show a selfless side.
"There is a great spirit in this group and they had to work hard for each other. I was very proud of them.
"Forest had a lot of momentum at the start and we had to switch our system before half-time and in the second half we were a lot better.
"We defended well, played our football and made sure that our goalkeeper didn't really have a save to make."
And Mackay had a special word for his match-winner, who rounded off an excellent 58th-minute move by producing a header from Peter Whittingham's inviting cross into the top corner beyond the reaches of Forest keeper Lee Camp.
Mackay added: "It was a fantastic header from someone who scores important goals in important matches. He's got a great attitude, too - there's no ego, just someone who wants the team to do well.
"When he came to the club he immediately bought into what we were attempting to do and he's as happy helping others to do well as he is scoring goals himself."
"I thought Rudy Gestede also merited a goal today for the overall performance he put in from start to finish."