The Tigers head to Tranmere Rovers tonight for their first assignment in a competition where they reached the semi-finals as recently as 2017.
Buoyed by collecting a first win of the season on Saturday at home to Reading, McCann is adamant that Hull can make progress in this season’s Carabao Cup.
“You want to have a good run,” said the Northern Irishman ahead of a tie in which he admits there will be changes to the City starting XI.
“At the start of the season when I sat down with the boys, I outlined what we want to achieve. Having a Cup run was one of the things I asked for.
“If it is the League Cup, great. If it is the FA Cup, great.
“If it is both then that is even better. We will try and go to Tranmere and get into the next round.
“This club has been used to cup runs, reaching the FA Cup final (in 2014) and things like that. It is in the genes.”
McCann proved no slouch in knockout football last term.
He steered Doncaster Rovers to the fifth round of the FA Cup for the first time since 1936.
This stirring run – which saw Rovers net 16 goals in just six ties before bowing out at home to top flight outfit Crystal Palace – also went hand-in-hand with success in the league, McCann’s side reaching the play-offs.
If he is to again make a two-pronged attack on success, the City chief appreciates getting past a Tranmere outfit very much on the up will not be straightforward.
“It is never easy going to Prenton Park,” added McCann. “Micky Mellon has done a tremendous job.
“Two promotions in the last two years. From the Conference to League Two and now League One.
“They have got a real winning mentality there and it will be a tough game for us.”
Matt Ingram is expected to start in goal, while Ryan Tafazolli and Matthew Pennington are pushing to be involved in defence. George Honeyman could also start for the first time along with striker Josh Magennis.
Last six games: Tranmere Rovers LWDWLL, Hull City LLDDLW.
Referee: S Stockbridge (Tyne & Wear).
Last time: Tranmere Rovers 1 Hull City 3; March 5l, 2005; League One.