As half-time approached, Peter McDonald looped a header towards Celtic keeper Fraser Forster that cleared the bar, then a Grainger corner failed to test the visitors' defence.
The Irish forced five corner kicks but the only test they gave Italian goalkeeper Gianluigi Buffon came off a free kick from 23 yards in the 79th minute that forced Buffon to dive to his right to make the save on Andrews.
The real domestic test may be around the summer corner should Rangers, Hearts or even Aberdeen, Dundee United or Hibernian provide a more capable challenge.