Roberto Mancini's men ran out fairly comfortable winners as goals from Sergio Aguero and Yaya Toure were enough to secure a win against the Hammers, despite a late reply from Andy Carroll.
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"I think Joe's back spasmed as he kicked a ball, he is a bit blocked up and will be a bit sore tomorrow but he will be OK on Monday," he told reporters.
"Most keepers, because they are throwing themselves about left, right and centre during the week will have issues around things like that. It is not much of an issue. It is a 24-hour thing."
Mancini's right-hand man suggested, however, that the back injury was to blame for Hart's part in Carroll's consolation goal as the England international failed to keep his compatriot's fairly tame strike out.
"It possibly affected him with the way he conceded the second," Platt added. "If you look at the ball when it has gone in, he can't get down to it."