Celtic manager Brendan Rodgers has already delivered his first trophy to the Glasgow club.
O'Shea remains positive about Sunderland despite a 2-0 loss to Liverpool at the weekend.
The Hammers players were pleased to get three points at Old Trafford.
Glasgow Rangers had the summer signing to thank as they came from behind to beat Partick Thistle.
Celtic beat Aberdeen 3-0 in the Scottish League Cup final on Sunday afternoon.
The 27-year-old impressed for Aston Villa on the weekend.
Leeds United visit Liverpool at Anfield on Tuesday night.
Divock Origi replaced Philippe Coutinho after the Brazilian was stretchered off in their 2-0 win over Sunderland and the Belgian opened the scoring.
Iwelumo played alongside the Sheffield Wednesday forward at Watford.
Manchester United and West Ham United drew 1-1 at the weekend.