Goals from Dan Burn and Joelinton secured a 2-0 quarter-final victory over Leicester at St James' Park and booked the Magpies their first last-four place since 1976, when they went on to lose in the final.
Howe, 45, was not born at the time and is relishing the opportunity to end a wait for domestic silverware which dates back to 1955.
He said: "It's too long, too long a wait. That's no criticism of anyone that's tried, but we're desperate to hurry up the processes and try to get the team successful as quickly as possible.
"That's easier said than done, and we now go to a semi-final. Getting to the semi-final is one thing, but you want to get into the final, you want to experience that.
"We know we'll have a huge test ahead of us whoever we get, but we're just delighted to be in there."
Asked if his side would fear anyone in Wednesday night's draw, Howe said: "I don't think fear is the right word. I think we respect whoever is left, but I don't think fear is right.
"The two-legged semi-final is a different dynamic, but we're just looking forward to it at this moment, and we'll start preparing when the draw is made."
Newcastle had to remain patient as first-half chances went begging, but got their noses in front when Blyth-born full-back Burn, who was released by the club as an 11-year-old, chose the perfect moment to score his first goal.
Joelinton added a second and although substitute Jamie Vardy might have dragged the visitors back into it, it was the Magpies who were celebrating on the final whistle, in Burn's case with an impromptu dance in front of the cameras.
Asked if he would be dancing should he end the club's trophy drought, Howe said: "Only my wife sees me dance - and she hasn't seen that for many years. I'm definitely not a dancer - rhythm isn't my strength."
Foxes boss Brendan Rodgers admitted the better side had won on a night when his side, who lost 3-0 at home to Newcastle on Boxing Day, had at times caused their own problems.
He said: "Listen, I think the best team won, the best team is through. We knew we had to start better than we did a few weeks ago and the players, to be fair, weathered that storm.
"The two goals, the first goal was soft - we've got the ball and give it away cheaply and then Dan Burn breaks into the box and scores, 1-0.
"Then we've got to really push, we obviously change the structure of the team, and the second one comes from a throw-in, so it was really disappointing.
"Vards has a chance to make it 2-1 which makes it interesting, but overall the team that played with the most quality and took their chances, they won the game, so congratulations to Newcastle."