Following the game, Parker faced the media where he spoke about his sides performance, Huddersfield, Bournemouth sustaining their levels of performance, Dominic Solanke and the game plan The Cherries had for the game.
On Bournemouth's performance
"From start to finish that was arguably one of our best performances of the season in every facet of what we did today.
"Our pressing, the intensity we played at, we stuck to the plan of what we prepared for this game and really executed it, we were clinical and fluid and I was delighted with that performance all round."
The Bournemouth boss was delighted with his team's display and it would be hard to argue with his pride for the performance.
Huddersfield had not lost at home since late November before Saturday afternoon, so the fact that The Cherries were able to win at the John Smith's Stadium so comfortably highlights their ability.
Whilst The Terriers were far from their best, it was a superb 90 minutes from Bournemouth, who dominated possession, had more chances than their opponents and they took the openings that they had to punish the hosts.
Parker was full of praise for all of his players, saying that to a man they were fantastic.
He was also pleased to see his game plan delivered in the exact way he had planned it in West Yorkshire.
Parker also said that should his side be able to produce performances of that ability every week they will be fine, presumably hinting at the idea that he believes his side can be promoted if they can be consistent until the end of the season.
"Huddersfield are a very good side and they've done incredibly well this season, what Carlos has done here is an unbelievable job.
"Today we was just too good for Huddersfield I think that's fair to say, we were clinical, we was clean in everything that we did and we obviously got the result."
Parker was very complimentary of his opposite number after the game, but in truth his side outclassed The Terriers on Saturday afternoon.
It was a frustrating afternoon for Huddersfield, who really failed to ever get going in the game, and needed to start the second half well to get back into the game at 0-2 down at the interval.
They instead conceded a wonderful flick by Solanke, which put the game beyond Huddersfield as soon as the game restarted.
The game petered out after that, as the visitors were happy to control possession and probe for any potential openings, which they did not force as much once they were three goals up.
He has now lost consecutive games in the Championship.
On sustaining Bournemouth's level of performance
"Today was the first time we got an all-round performance really, I think we've sat here and said that we've had it in spells where we've really dominated but today we were superb.
"It's definitely a boost for us and to come here given where Huddersfield are and how well they've done and put a performance like that in is a massive boost for us really."
Bournemouth were fantastic throughout the tie at the John Smith's Stadium, for the whole game they looked the most likely to score.
They took most of the opportunities they created and also were able to limit the chances that their opponents had on Saturday afternoon.
Nobody left the stadium after the game complaining that The Cherries had been fortunate to take all three points, as they were far superior to The Terriers on the day.
Parker referenced the fact that Bournemouth had been able to dominate a game against a side who have been superb in the league of late, which could perhaps show Bournemouth's potential to secure automatic promotion.
Chants of 'we are going up' from the away end towards the end of the game shows the confidence Bournemouth fans have in their side returning to the Premier League next year.
"He was incredible, I don't just want to call out individuals, but his goals are clear for everyone to see and his all-round game today and his work ethic [were fantastic].
Dominic Solanke produced a wonderful performance once again for The Cherries, in what has been an impressive season for the £17m signing.
He got the assist for the first goal scored by Anthony with a driven cross into the box which gave Anthony a tap in, and scored his 23rd of the season with a beautiful flick past Lee Nicholls.
His physical presence being able to win headers and hold the ball up caused The Terriers' backline all sorts of problems for the whole afternoon, and Parker's praise for the number nine reflected that.
With Aleksandar Mitrovic sitting on 35 goals in the Championship this term, Solanke may not be the best goal scorer in the league, but what is certain is that he is a pivotal player for Parker's side.
On Bournemouth's game plan
"We're on a journey here and a ride, we've done incredibly to be where we are really and we need to play freely really.
"It was a constant message all week and it was a constant message at half time as well we need to stick to what we're doing, we're not holding onto anything here."
Parker was happy with the way his side were able to deliver the plan which he had drawn up to beat Huddersfield on the training ground.
It was not hard to see why he was pleased, as it was a structured and calculated showing from Bournemouth, who were able to create several chances in the first half in particular and did a good job of taking them.
They also limited the hosts to very few, insignificant opportunities at the other end.
Overall, it was a top drawer win for Bournemouth and an emphatic response to their recent dip in form after only picking up one win in their last four games prior to facing The Terriers.
Parker admitted that it is the home straight of the season, and if The Cherries can play like that every week, they will have no problems with being promoted back into the Premier League.