Boro have been on the march in the npower Championship and four successive wins have kept them on the coat-tails of leaders Cardiff.
But they turn their attention away from their quest to return to the Barclays Premier League at the Stadium of Light and are on the hunt for revenge after losing to the Black Cats in the FA Cup last season.
"It's a game we are looking forward to, we went there last year and gave a decent account of ourselves. We were disappointed not to come away from there with a win," Mowbray said.
"But it's the next game for us, there's no points at stake and it is a nice break from the pressure of going for three points.
"It's a game in which the supporters and the team will want to go there and give a good performance and get a victory.
"It would be nice to get to the quarter-finals of a major tournament but it will be a big ask at a Premier League side.
"It is a big job for us, but we will go and give it our best shot."
The clash, in which Sunderland's manager Martin O'Neill is expected to make changes, will be Boro's fourth game in 10 days and Mowbray is also considering swapping his team around.
"We are going to change the team around and give some of them a breather," he added.
"We are trying to get a balance between trying to make sure we don't pick up any injuries in another intense game and doing well, so we are going to put a team out that will be very competitive and try and get a result."
Mowbray will run the rule over Jonathan Woodgate and Marvin Emnes.
Defender Woodgate has missed the last two games with a thigh injury while Emnes limped out of Saturday's 2-1 win over Bolton with a hamstring problem, and both men will face late fitness tests.
Merouane Zemmama is back in training having recovered from a hamstring problem and he is expected to be in the squad.
There is no movement on the remainder of Boro's injured contingent, with Luke Williams (hip), Kevin Thomson (calf), Rhys Williams (ankle), Lukas Jutkiewicz, Mustafa Carayol and Curtis Main (all knee) still occupying the treatment room.
Boro have a good record in the League Cup, having won it in 2004 and finished runners-up in 1997 and 1998.