Poyet's bottom-placed side were 2-0 down with just seven minutes to play on Saturday, but Steven Fletcher and Jack Colback earned them a 2-2 draw, with the latter finding the net with a deflected effort in the fifth minute of stoppage time.
The midfielder's effort struck Cardiff captain Steven Caulker on its way past David Marshall, and Poyet was glad to get some fortune after seeing his side score six own goals in their last 14 games in all competitions.
"I am delighted we scored a deflected goal for the first time in a while, because it (luck) was always against us," he said. "It was time to get a little bit of luck and get a lucky goal.
"It looked difficult, but in the last 25 minutes there was only one team on the pitch, we were coming and coming and coming, and knocking on the door.
"It was a matter of scoring the first goal with time to go on and score the second. Sometimes you don't give yourself another chance.
"We are never going to give up, to beat us you are going to have to be very good or you are going to have to fight very hard because we are going to fight to the end."
The draw moves Sunderland two points adrift of safety and extends their unbeaten run in the Premier League to four matches.
