It had been 192 days since Newcastle ended their trophy drought with their Wembley triumph.
And that landmark win against Liverpool only made them hungrier for further success.
There was certainly no chance of Howe having one eye on the visit of Arsenal at the weekend and underestimating in-form Bradford in front of a near sell-out crowd at St James’ Park.
No wonder, then, as Sven Botman, Malick Thiaw, Lewis Hall, Bruno Guimaraes, Joelinton, Anthony Elanga and Anthony Gordon started on Wednesday night as the Newcastle head coach made seven changes from the weekend.
It showcased the depth of his squad and a side that has struggled in front of goal rediscovered their scoring touch against third-tier opposition.
Indeed, Newcastle scored as many goals in the opening 19 minutes of this tie as they had in their previous four fixtures combined.
However, it could have been even more comfortable as Osula, Gordon, Guimaraes, Elanga and Joelinton all had further opportunities.
When Joelinton claimed the third goal, supporters on the Gallowgate End were chanting: “We’re Newcastle and we’re going to win the cup!”
Danish striker Osula’s late effort took his tally to three this term and will boost his confidence.
But the 34-year-old Cook, who grew up idolising Alan Shearer and returned recently after an anterior cruciate ligament injury in January, gave Bradford’s 4,900 fans a moment he, and they, won’t forget with a venomous strike.
They had their moments, but never looked likely to cause a shock and Graham Alexander’s side will turn their attention back to League One and a promotion challenge.