The Sunderland manager has worked wonders since replacing Steve Bruce at the helm at the Stadium of Light in December, transforming the Black Cats' Barclays Premier League fortunes and raising hopes of an extended cup run.
Mowbray will attempt to inflict a rare bout of misery on the Ulsterman in Wednesday's fourth-round replay at the Riverside Stadium, but admits he is envious of his counterpart's secret ingredient.
He said: "Everybody in football looks at Martin and thinks, 'What is the ingredient?', not just me, anybody.
"Steve Bruce is a good, honest, hard-working Premier League manager, and yet Martin O'Neill has come in and found some magic dust from somewhere to sprinkle over the same group of players and get results you can only dream of in all different types of ways.
"I watched them play Manchester City on the telly, which possession-wise was a mismatch, really.
"Manchester City are a high-quality, very expensively put together football team and yet Martin and his team found a way to win the game.
"Martin seems to have the ingredient where he can find a way of winning games, which is a great quality for any manager to have, to be able to influence a football match."
For much of the first game, Mowbray's men were more than a match for Sunderland, and while injuries threaten to rob the Boro manager of up to five of the men who started at the Stadium of Light, he is determined to make life just as difficult on Teesside.
He said: "It's a great challenge for us, a great test. We have to make sure we give Sunderland some problems and ask some questions of them.
"Sunderland are a team with some dangerous individuals - the boy (James) McClean is catching the headlines at the moment, coming off the left wing and looking a real threat.
"Fraizer Campbell has come back from injury and scored two in two, and he is a quality player, of course.
"(Stephane) Sessegnon can light up any football match in the Premier League or the FA Cup.
"We are mindful of the talent they possess, and yet we coped reasonably well last Sunday and I hope we can do that again."
Mowbray will be without striker Scott McDonald, who could miss up to 12 weeks with a knee problem, as well as keeper Danny Coyne, midfielders Nicky Robson and Merouane Zemmama and striker Bart Ogbeche, while Barry Robson, Faris Haroun and Marvin Emnes will be assessed before the team is named.
He said: "It is a case of naming 11 players and then dragging some youngsters over and sticking them in and around it.
"We will see. Listen, there will be a team out there and it will be very competitive, I am sure."