Irwin needed to win their last two games to join Adelphi in the semi-finals but lost by 52 runs.
In the game played at Roehampton, the home team made 184 for four off 34 overs then bowled out Irwin for 132.
In the August 1 semi-finals, MBCC will meet West Confed while Williamsfield will meet Adelphi.
West Confed and Williamsfield topped Zone A with 42 points each while Adelphi were tops in Zone B with 45 points. MBCC finished with 36 points, the same as Champions Sports Club but MBCC scored more runs during the season.