The Hammers seemed destined to leave St Andrews with maximum points after Frederic Piquionne and Valon Behrami had given them a 2-0 lead.
However, goals from Cameron Jerome and defender Liam Ridgewell salvaged a point for Blues against the Premier Leagues bottom placed side.
"We're disappointed to drop points at home," the Blues boss told Sky Sports after the game.
"We lacked penetration in the first half and never had that cutting edge until we went two goals down.
"Thankfully the guys' resilience and steel shone through and we could have won it in the end.
"The substitutions were good for us," he added.
"Craig Gardner came on and did a great job and Jean Beausejour looked pretty good.
"He looked hungry and eager and there was a good tempo from him. The only thing he lacks is match fitness."