The Wembley showpiece finished 2-2 after extra-time before both Gerrards missed spot-kicks, but it was Anthony's which proved crucial in sudden death.
Steven Gerrard told BBC1: "It's always cruel when it comes to penalties, but there has to be a loser.
"It was always going to be that one of us was sad and one celebrating. I've got mixed emotions. Obviously I'm delighted to win the cup for our supporters, but I feel for Anthony and Cardiff.
"It doesn't matter what I say to him - he's going to be down. I'll be there for him and all the family will be behind him."
Veteran Reds defender Jamie Carragher admitted Liverpool were overdue a major trophy.
"It's been too long since we've done it, really, and hopefully this will be the first of many to come," he said.
"Wembley is Wembley. We had some great days in Cardiff but I don't think anything beats Wembley. It's fantastic, hopefully we can come back again this season."
Liverpool manager Kenny Dalglish was just pleased to have clinched the cup, regardless of how it was done.
"It's a long way to win it, but our name's on the trophy and that's all that matters," he said on BBC1.
"I thought the boys played particularly well. Cardiff were always going to be difficult but at the end of the day we've got our name on the trophy.
"We were always going to be under pressure. They have very good delivery from set-plays and they were never going to lie down. They were a great credit to Cardiff today [Sunday].
"It's not a nice way to win a cup, but we'll take it."