The Cottagers won 2-0 in the first-leg and almost were down 2-1 at home on Thursday, but held on to book a meeting with Brentford at Wembley.
"Overall we've got ourselves to the final, an incredible achievement in terms of a long drawn out season, the 48th game that was tonight," said Parker.
"The goal was to get to the final and we have done that. The performance and where we were was tough. Cardiff made it very difficult for us, coming here like a wounded animal after the first leg and had nothing to lose, in that sense. You see the difference between the two teams, a bit of an edginess to us, goals change that complex. They had nothing to lose. We sensed that, the way they play they constantly put you under pressure from all over the pitch.
"At times we didn't deal with that well enough. We would be the first to admit that, in the end it was about mentality and a mindset and that is what is was, roll your sleeves up because at the end of it is a massive prize and that's the final. We all want it, a chance and an opportunity to get into the big league. In those moments you have to have a desperation to do all you can, big players have to step up."