Should they reach that far, they will face another stern test in Manchester United.
On Wednesday, the Teessiders will first have to face Rafael Benitez's men in their delayed fifth-round tie at the Riverside hoping to claim another Barclays Premier League scalp after dumping neighbours Sunderland out of the fourth round of the Capital One Cup.
However, Mowbray is acutely aware of the threat posed by the Blues even if Benitez chooses to shuffle his pack, and has told his side only hard graft will give them a chance of containing them.
He said: "When you haven't got world-class players, you have to first and foremost have a work ethic. You have to try to condense space, you have to try not to be isolated one-on-one in certain areas of the pitch.
"And yet, you have to balance that off with having an attacking threat. You have to have a way of trying to score a goal and if you have everybody back, it's very unlikely you are going to have too many attempts. That's the balance for any manager.
"Watching Manchester City at the weekend, it was 'You have an attack, we have an attack and see how can hurt the opposition the most'.
"I would have to say, we won't be playing like that because I doubt we are going to leave three up front and wait for our defence to give it back to them and we attack them and they all run back.
"That's the difference. Athletically, we have to cover more ground than they do. They can rely more on their technique and their talent to pick the right pass."
Boro will head into the game having won only one of their last nine npower Championship fixtures, a run which has seen them slip out of the play-off places.
But it is Mowbray's opposite number Benitez who will head into the contest knowing failure will pile the pressure on to him with his detractors becoming increasingly vociferous.
However, the Boro manager is wary of the strength which can emerge from adversity and believes the Spaniard's track record proves he can handle the heat.
He said: "In adversity, the group of players should be feeding off that and becoming stronger and more unified, and I am sure that's happening at that club.
"The decision for Rafa to take that job was made because he is a top manager who has won European trophies, who has won leagues in just about every country he has been to.
"He is a good football man. I don't know him well, but I have been in his company and he loves to talk football tactics.
"I have only got respect for Rafa Benitez. It is a tough job, of course, but he seems very professional, long in the tooth regarding his job from the point of view of getting on with his job and trying to win trophies for the club.
"Every football manager at times feels the wrath of the support and you have to be very, very single-minded to sit in a football manager's job in 2013 because of the social media aspect of the world now, everybody can do your job, everybody has got an opinion.
"You have to be single-minded and I think Rafa is showing everybody he is pretty single-minded, getting on with his job, trying to win games.
"Whenever he loses, it's probably his fault; whenever they win, nothing is said. You do need a thick skin."
Mowbray will be without injured duo Jonathan Woodgate and Lukas Jutkiewicz, while Josh McEachran, Kieron Dyer and loan signing Sammy Ameobi are ineligible for the tie.