Limerick finished with 14 players after David Breen was shown a second yellow card seven minutes from the end. Breen had scored Limerick's first goal after 24 seconds and they led 2-8 to 0-5 at the interval.
Allen said: "It was a good first half and we could have had more goals, but we lost our way in the second half. Admitting that Tipperary will be a different challenge next week," Allen said: "It is a work in progress as we try to ensure that our best side will be on the field in June."
Mary Immaculate make their Fitzgibbon Cup debut next month and manager Eamonn Cregan was pleased with the performance.
Breen's early goal settled Limerick and when Shane Dowling had the first of his two goals after 23 minutes. John Conlon kept Mary I in touch with four frees (0-5 in total).
Scorers – Limerick: S Dowling 2-5 (0-4f), N Moran 0-4, D Breen 1-0, C Allis, K Downes, D Reidy, S Hickey, T Quaid, S Tobin 0-1 each. Mary Immaculate: J Conlon 0-5 (4f), C Galvin, S Curran 0-2 each, B O'Halloran, L Considine, D Hannon, L O'Farrell 0-1 each.
Limerick – N Quaid; T Condon, R McCarthy, S O'Neill; C King, W McNamara, G O'Mahony; D O'Grady, J Ryan; D Breen, C Allis, N Moran; S Dowling, K Downes, S Tobin. Subs: D Reidy for Tobin (ht), T Quaid for Allis (48), S Hickey for O'Grady (51), R Egan for Ryan (56), T O'Brien for Downes (58).
Mary Immaculate – N Carrig; K Fennessy, R O'Donnell, M McGrath; E Hogan, D Hannon, D O'Carroll; L Considine, C Galvin; S Curran, W Hickey, B O'Halloran; E Hogan, J Conlon, L O'Farrell. Subs: M O'Connell for E Hogan (57), A Cagney for McGrath (60).
REF – D Fox, Clare.