The Australian was thrown into the deep end with first-choice keeper Pepe Reina and his replacement Alexander Doni both being suspended for the crucial match against the Toffees.
But the 30-year-old was able to help Kenny Dalglish's side progress to the final and attempt to win their second piece of silverware this season.
Jones, speaking to BBC Radio Merseyside, said:"It's a brilliant feeling to come to Wembley, be a Liverpool player and get a win.
"I'm just glad that I can be a part of this season. Hopefully the boys can go out there and win another trophy."
The League Cup winners went down to an early Nikica Jelavic goal, but second-half strikes from Luiz Suarez and Andy Carroll secured victory over David Moyes' team.
The match was only Jones' fourth appearence for Liverpool since moving to Anfield in the summer of 2010 and he insists he was suitably prepared for the occassion.
"As a goalkeeper, the downside is that you don't get the chance very often, but when you do, you've got to be ready," said the former Middlesbrough stopper.
"It's been difficult but you've got to cope with it, go out there and do your best."
Jones added that his son Luca, who died after a battle with leukaemia in November, was a huge source of inspiration for him on the day.
"He was on my mind for the whole game," said the Australia international. "He was my biggest fan and always proud of me.
"The Liverpool fans have been unbelievable. I'm not the most important player at the club but they treat me really well and I can't thank them enough. It shows the sort of club Liverpool is."
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