The Championship side head to top-flight Swansea in the quarter-finals of the Capital One Cup on Wednesday night dreaming of a place in the last four and the chance to repeat their triumph in the competition back in 2004 under Steve McClaren.
However, Mowbray makes no bones about his priorities for the season and, while he is determined to take the club he supported as a boy as far as he can along the road to Wembley, a return to the big time is the major prize in his sights.
He said: "Whilst it's nice to have a run in a cup competition, get the plaudits and potentially get to a semi-final, televised games and heighten the profile of your club, the bottom line come May is, if you don't finish in the top two or the top six, giving yourselves a chance, it's a wasted season.
"For the club, the ambition we have got is to try to get back there as quickly as we can."
To that end, Mowbray will not allow the cup campaign to act as a distraction.
Indeed, his determination not to allow the league campaign to falter - the Teessiders currently sit in third place in the table - means preparations for Saturday's clash with Wolves have dictated their travel arrangements back from South Wales.
He said: "I am not that sentimental. Who were last year's semi-finalists? It doesn't matter. It matters when you stick your name on a trophy, then we could say what we had achieved.
"Our main target is to win league matches. When you are this close in a cup competition, you don't pick weakened teams, you pick your best team or your strongest team available to go and try to win.
"But I am still very, very conscious of the preparation for Saturday, which is why we are staying over rather than getting back at 5am so the players can get a decent night's sleep.
"They can cool down in South Wales and then they can get themselves back and we will prepare on Friday.
"We want to win every game, and yet realistically you can't win every game. But we will try to win the next game in front of us, which is Swansea."
Having dumped derby rivals Sunderland out of the competition at the Stadium of Light in the last round, a trip to the Liberty Stadium - Boro's 12th successive League Cup tie on the road - holds no particular fears.
However, Mowbray is well aware of the quality at opposite number Michael Laudrup's disposal.
He said: "I have to say this Swansea team is a pretty special football team with the ball, they are very, very good.
"To go to the Emirates and win 2-0 and out-pass Arsenal as they did is quite a feat, so we have total respect for what they do.
"I don't know what the betting is, but I can only imagine today, if you are a betting man, I am sure Swansea are pretty odds-on favourites to get through.
"And yet if we were sitting here playing Bradford at home tomorrow night we would be pretty odds-on as well and you could be almost talking past that game to a semi-final.
"But I won't allow the players or my mind to get anywhere near any semi-finals because we have got Swansea City, who have just beaten Arsenal and West Brom, away.
"I have watched them and they have got some good players, so we will need to be at our very, very best to try to progress."
Don't miss any live and exclusive football coverage this festive season. Click here to visit Sky Sports' Festive Calendar