Howe praised the Clarets for the way they responded to the concession of an early goal despite having four players away on international duty.
But he was not happy with Burnley's second-half display when it needed a couple of splendid saves from goalkeeper Lee Grant to keep their League Two hosts at bay.
Howe said: "Our response to Vale's goal was very pleasing because we controlled the rest of the first half and scored three good goals from our perspective.
"The boys played some good football and got well on top, but it was a different story in the second half when we had to defend well to see it through.
"Lee (Grant) made some good saves and I was pleased for him, but we should have seen the game out better and we've got to improve in that respect. Vale got into us and we didn't deal with it as well as I would have liked.
"We needed to be more composed on the ball and better in our decision making. The Championship is a tough league and we will need to keep the ball better than we did.
"I know we were without four of our strongest players because of the internationals, but we all must keep striving to improve and I'm confident we will do."
Cash-strapped Vale had to play in an off-the-peg pink strip as their administrators delayed ordering a new kit because of the club's ongoing financial problems
But they took the lead through Chris Shuker's free-kick before Burnley fought back through goals from Chris McCann, Charlie Austin and Dean Marney.
To their credit, Vale refused to roll over in the second half as Shuker and Louis Dodds twice came close to reducing the arrears and Micky Adams was encouraged by their efforts.
Adams said: "We were a lot better in the second-half when I was pleased with them.
"We put Burnley under pressure, created chances and forced their 'keeper to make some good saves.
"With the greatest respect, we were never going to win this cup and in our division we won't come up against the calibre we've faced tonight. There were some encouraging signs which we can build on."