Manager Vickers said: “I thought the performance was great, especially after playing 180 minutes within a few days.”
Town came from behind to clinch their first win over Bradford in more than two years - Kate Mallin, who scored her 10th goal of the season with a penalty, and Emily Heckler got the goals.
Heckler, back at Town after a short spell with divisional rivals Fylde Ladies, followed up with a hat trick against Derby.
She netted with a looping header from a 27th-minute corner, and five minutes later, fired home direct from a free-kick.
Heckler took advantage of defensive sloppiness by Derby to score her third just before the break.
Sarah Dobby headed home on 84 minutes before Derby claimed a consolation goal.
“It’s great to have Emily back,” added Vickers. “She didn’t have a pre-season but is getting fitter through hard work on her own.
“It was about easing her back in - after all we have a lot of new players - so we gave her a few substitute appearances to begin with.
“She is a class act who has set the bar high in the past.
“Emily is up to nine goals already this season, and when you have someone like her in your side you’re laughing if I’m honest.”
Vickers is also pleased at how his team, who made a sluggish start to the season, are learning game management.
“It was always going to take a little bit of time. Even though the performances were there in places, they weren’t whole,” he explained.
“We would get 60 minutes before concentration levels dipped but the girls are working hard to improve things and it’s paying off.”
Next up for Town is an FA Women’s Premier League Plate second-round tie at Guiseley Vixens on Sunday (2.00).
Town’s second string were 4-1 winners in their FAWPL Reserve Northern Division clash at Bradford City - next up for them is Blackburn Rovers at home on Sunday (2.00).
Town’s academy team head to Dinnington Town on Sunday (2.00) for a Sheffield and Hallamshire Women’s League match.
Meanwhile, the Under 18s romped to a 21-0 win at home to Handsworth in the Sheffield and Hallamshire Girls’ League with six goals apiece for Amy Broomhead and Ella Harris.
Millie Morris (2), Laura Walker, Isobel Boothroyd, Tara Duce, Eleanor Smith, Jodie Lodge, player of the match Faye Allen and Ellie Womersley also scored.
Town head to Chesterfield Ladies on Saturday (11.00).
There was also a big scoreline for the Under 15s, beating visitors Barnsley 9-0 - Courtney Livesey (4), Macy Ellis (3), Harriet Waller and Jess Barrow scoring for Town, who host Wisewood Juniors on Saturday (10.30).
However, the Under 13s suffered their first defeat of the season, 3-2 at Sheffield Wednesday - the home side leading 2-0 before player of the match Tamara Wilcock scored for Town.
Wednesday then made it 3-1 and although Laura Hulme pulled one back, Town couldn’t force an equaliser.
It’s a trip to AFC Pogmoor next on Saturday (11.00) while the Under 11s are at home to Crosspool Juniors (1030).