The 26-year-old, who has struggled with injuries this season, had to be substituted due to a calf problem after just 33 minutes of the fourth-round tie.
With the Citizens travelling to Queens Park Rangers on Tuesday, Platt revealed Kompany won’t recover in time for the must-win clash at Loftus Road.
“He has pulled his calf. We won’t know how bad it is until the morning but there won’t be any chance of Tuesday,” said Platt.
City had the better of the chances at the Britannia Stadium, with David Silva hitting the woodwork in the first half, before stand-in skipper Pablo Zabaleta netted the winner in the 85th minute.
The Citizens had only managed 1-1 draws in their last two trips to Stoke ahead of Saturday’s tie, and Platt was pleased to see the defending Premier League champions keep a clean sheet.
“The pleasing thing is we battled hard, defended well and kept another clean sheet,” added Platt.
“It is pleasing from that perspective and it is also pleasing to go through.
“We knew it was going to be difficult here. You know the ball is going to come in the box and you’re going to have to compete for first balls, second balls all day.
“It is the way it is going to be and I thought we did it well.”