Darren O'Dea captained Celtic into the fifth round of the Scottish Cup last night thanks to a goal from Niall McGinn against First Division Morton.
Celtic will travel to face Stenhousemuir or Dunfermline in the next round with the SFA facing an appeal from Dunfermline against their expulsion for fielding a suspended player as a substitute in their 7-1 win.
O'Dea was paired with Glenn Loovens in central defence as speculation continues that Arsenal's Philippe Senderos is on his way to Celtic on a loan deal till the end of the season.
McGinn was brought in to the side to replace the injured Ki Sung Yueng and took full advantage of the opportunity by scoring the decisive goal in the 35th minute when he converted a cut-back from Marco Fortune from 10 yards out.
The failure of Fortune and Georgios Samaras to find the net against First Division opposition will be a concern for Mowbray whose transfer window activity has been concentrated on defenders so far. After the match the Celtic boss said: "It was a competitive game and we knew that would be the case, but it's 'job done' for us.
"In cup football you've got to get in the next round and we've done that. There were a few too many balls bouncing over our heads in the first half for my liking.
"But in the second half we saw it out pretty comfortably, and they didn't trouble us too much.
"Again tonight we missed some good opportunities and we need to be more clinical to make the scoreline reflect the balance of play. We worked hard to get a second goal and it didn't come, but we didn't need one. I don't think it was as fluent as the last few months but I don't think that was ever going to be the case."