City manager Dave Jones was upset with his side's overall performance.
"These are the type of games you have to see out and we had the chances to do that yet we never showed the creativity we are capable of and we have been caught by a sucker punch," he said.
"This division is a difficult one but we should still have been good enough to win and it is very disappointing to lose a game like this.
"You could see it coming and three individual errors led to the goal. They were waiting for one opportunity and when it came they took it.
"There is no reason why we couldn't have taken a win as we warned the players that it would not be easy, but when you miss chances like those we had early on then it causes problems.
"Passes were over-hit, chances missed and we just didn't do it today and we have to quickly correct that.
"It was a good opportunity for us but we have missed it."
Paul Mariner saw Argyle score for the first time in nearly nine hours of football.
"We worked very hard for that result but the signs have been there for a couple of weeks," he said.
"The players want to get this club out of the mess we are in and we knew we would get a resilient performance from them but three points is a wonderful result.
"The away support was remarkable and I felt we created a few chances in a very tight game but we needed that little bit of luck.
"To keep a clean sheet against such a high powered attacking force as Cardiff have is a magnificent effort.
"We haven't scored for a long time but you have to go back to the basics and that is what we have done today."
