The 3-0 win hands Hughton's men a trip to the Hawthorns on January 23, five days after the Baggies head for Tyneside and a Championship promotion showdown.
Hughton said: "It's a big week, and it's a big week for both clubs. I suppose it will be a fair indication for where we both are at the moment.
"Of course, our priority at the moment is the first game here at St James', and it's one that will give us a massive boost if we are able to win it."
If the league game will be the overwhelming priority for Newcastle, they will hope to keep their FA Cup run going after extending their unbeaten sequence to 13 games with a regulation victory over Argyle.
They were hardly taxed as they eased into the fourth round, and although it was Lovenkrands who deservedly claimed the headlines with a well-taken hat-trick- he was pushed all the way by some of his team-mates.
Jose Enrique and Jose Gutierrez caused the visitors so much damage down the left that a boxing referee would have stopped the contest long before Andy D'Urso blew the final whistle.
The Argentinian was the provider in the first half, sliding a perfectly-weighted 10th-minute pass into the Dane's path to allow him to lift the ball over keeper Roman Larrieu, and then crossing for Lovenkrands to head home the second five minutes before the break.
Newcastle had to wait until the 72nd-minute for their third goal, and this time it was Kevin Nolan who crossed for Lovenkrands to volley past Larrieu after Andy Carroll had headed a cross down to his feet.
Hughton, who reported no significant developments on the transfer front, said: "The objectives were to win the game - if it was possible to do that with a good performance, then even better, and even better still if we came through unscathed with no injuries.
"All three of those, we have managed to do."
Plymouth boss Paul Mariner, who admitted after the game that new Burnley boss Brian Laws wants to take his assistant John Carver to Turf Moor, was full of admiration for Lovenkrands' contribution.
He said: "His timing of his runs is pretty special and his first goal, his finish was fantastic.
"He has a lot of composure in the box. When everybody was getting excited, he was the coolest guy and just chipped it over the keeper. I thought he was terrific."