Adam Baker’s brace led Albion on their way to the third round in a one-sided evening at the i2i Stadium on Wednesday night.
Josh Barrett and Nick Black were also on target in the 4-1 victory, with Worksop right-back Steve Wolley adding a late consolation to the scoresheet.
Miller said: “The biggest thing about tonight’s result was that we were playing one of the teams that will be there or thereabouts come the end of the season.
“We needed to send a clear message.
“The lads have been absolutely superb. They adapted to the conditions a lot quicker.
“The game plan worked really well and but for their ‘keeper doing really well, it could have been a lot more.
“The lads have worked really hard. It’s a great set of lads. The cohesion in the dressing room is absolutely phenomenal at this moment in time.
“We have worked hard to get the club where it is, and to be top of the league and now into the FA Vase third round, they deserve it.”
Albion reached the quarter-finals of the national competition under Paul Marshall 12 months ago, and Miller has made no secret that he wants to emulate his predecessor’s run.
But to achieve that feat, Albion must first overcome a trip to Northern League outfit Sunderland RCA in the third round on December 12.
Sunderland lie eighth in Division One, just 12 points off top of the table Morpeth Town.
And Miller was in no mood to get carried away about his side’s chances of reaching Wembley.
The Brewers boss added: “We have to take each round as it comes.
“The problem with cup football is, you could be dominating and their keeper has a brilliant day. In the 89th minute you score an own goal and you go out. It’s ruthless.
“But I think we’ve built a squad good enough to have a good go.”
The second round tie was eventually played 15 days after originally scheduled, following flooding to the pitch at the i2i Stadium
Miller hailed the ‘army of volunteers’ who helped clear the pitch, a process which had been delayed due to the presence of fish on the field.
Garforth Town’s chairman Brian Close was among the helpers clearing the pitch of leaves on Wednesday.
“It’s a massive reward for anyone that has given up any minute of their time,” Miller said.
“They’ve worked really, really hard to get the game on and then to see us beat one of the best teams in the league like that, it’s a great reward.”
Sections of the Worksop support had complained about the delay to the match, with some believing it should have been rescheduled to take place at the Tigers’ Sandy Lane ground.
But Miller rejected the idea the visitors had reason to grumble.
He added: “If you spoke to their owners, they have been kept fully in the loop.
“The relationship between the two clubs is really, really good.
“In these circumstances you get sympathy because it’s something that was completely out of the club’s control. It was so frustrating to look across the pitch and see all the hard work that has gone into the football pitch, to see the football club under that much water.
“You see it on the TV and you don’t expect to see it in your own back yard. You never know when it’s going to happen again.”