The npower Championship side travel to Swansea in the last eight this evening hoping for a repeat of their victory over top-flight opposition in the last round at neighbours Sunderland.
However, if they are to achieve that, they may have to find a way to stop striker Michu, who has made a blistering start to his career in England.
The 26-year-old Spaniard, a £2million summer signing from Rayo Vallecano, currently leads the top division for goals scored having plundered 12 already, and that makes him a major threat to Mowbray's men.
The former central defender said: "He plays in that 'ghost' position behind a striker, and who's marking him?
"He can drift into areas and he's got a fabulous intuition to get into goalscoring areas unnoticed.
"He's a big physical presence, so he can jump over the top of people, he is obviously very clinical with his finishing.
"For £2million, you would have to say he has been just about the buy of the season.
"We will get a feel of him tomorrow - I am sure he will be playing and we will feel ourselves the threat he poses."
Home advantage and loftier status will guarantee that the Swans run out as firm favourites to progress, but while Mowbray freely admits promotion to the Premier League is the Teessiders' overwhelming priority for the season, he insists they will do all they can to reach the last four of a competition they won in 2004.
The Boro boss is confident he too has firepower at his disposal in the shape of Scott McDonald, Lukas Jutkiewicz, Marvin Emnes, Emmanuel Ledesma and Ishmael Miller.
However, with a vital league clash with Wolves to come on Saturday, he has warned his hitmen that some of them will be kept in reserve.
Mowbray said: "If any one of our strikers doesn't play, there's a fair chance he is going to play on Saturday.
"I'm using it to say, 'If you want to be angry, be angry. If it's a fatigue thing, save your legs and get ready for Saturday'.
"I will tell them two days in advance that they are playing on Saturday - I might even tell them today that they are playing on Saturday just to make sure they are ready and they understand that they are not dropped, they are not being left out because they were poor.
"Everybody is required to play and you are just utilising your squad, particularly in our forward area.
"If you have got five or six players who you know can do the job, you can pick players to win matches and pick combinations against different types of defenders.
"As long as they understand that and don't think you are giving them manager-spiel, then I think it works fine.
"Generally this season, more often that not, it's been okay. We have scored a lot of goals and generally won games."