Just like in the Carabao Cup final back in February, Liverpool needed penalties to see off Thomas Tuchel's side following a goalless draw after extra-time.
The victory ensured Liverpool's hopes of winning an unprecedented quadruple is still alive.
Liverpool went into the game without an injured Fabinho, while Mohamed Salah could not complete the first half and Virgil Van Dijk played no part in extra-time.
It was Liverpool's first FA Cup triumph in 16 years, ensuring manager Jurgen Klopp has won every available club honour in his time at Anfield.
Captain Henderson, who was the only surviving member of the last Liverpool side to play an FA Cup final back in 2012 when they lost 2-1 to Chelsea, was impressed with how his side went about their business at Wembley.
"It was difficult, we knew it would be," the England international told BBC Two. "We've had so many games in a short space of time.
"It was a big blow with Mo going off and Fab last week. But that's what we're all about, the attitude and mentality to keep going and to dig in when it's tough.
"We're here to lift trophies, we work so hard all season. To come here and get over the line means a lot to everyone. The fans deserve it, the whole club.
"It's a big moment for us, we haven't been in this final for some time so to win it was special. It's fine margins, especially in finals, as we know in the last two.
"We've just got to give everything, like we always do. We've got to work for each other and play with the players that we've got.
"It's incredible some of the talent we have got in the dressing room and the personalities. You put that together and you win trophies really."
"We've won two so far this season. We've still got some big games left. We just need to keep on going right until the end and see what we can finish on," Henderson added.
"We've got to recover quickly, another big game on Tuesday against Southampton, we have to be ready for that. Then [it is] Wolves at the weekend, and then the Champions League final.
"We have three big games left and hopefully we can win all three and finish the season on a high."
