Scotland blew the chance to equalise just before half-time when they were awarded a rather soft penalty, German referee Babak Rafati deciding Daniel Lafferty had fouled KevinMcDonald.
Midfielder KevinMcDonald was fined after he left Turf Moor without permission after he was substituted at half-time of the 6-1 mauling by Manchester City on 3 April.
Owen Coyle's side, inspired by the outstanding Chris Eagles and KevinMcDonald, more than matched Arsenal for long periods and looked the more likely winners for spells in the second half.