Pablo Zabaleta struck from close range after 85 minutes as City, who had been dominant in the early stages, finally wore their resilient hosts down.
Platt said: "The pleasing thing is we battled hard, defended well and kept another clean sheet.
"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."