Warwicks had been set 441 to win and were doing ok with their overnight score of 263-6.
Jon Trott and Neil Carter kept totting up the runs but when Carter went for 73, Imran Tahir and Andrew Miller were both out cheaply.
Trott had taken his score to 150 but when he was caught by Croft off the bowling of Mahmood, Warwicks were all out for 375, some 65 runs short.
Warwicks are at home to Hampshire in a Pro40 game at Edgbaston on Saturday.