A late Edin Dzeko goal earned City a vital three points at The Hawthorns, completing a comeback produced despite playing the majority of the match with 10 men.
Platt thinks that being able to recover from James Milner's red card to earn a last-gasp victory shows the strength of character at the club.
He told BBC Sport: "It was a strange game which was full of incident.
"We thought we controlled the first half, despite going down to 10 men, and it was tremendous how we stuck together in the second half and created so many chances. It's a great fillip to win after playing for almost 70 minutes with 10 men."
Dzeko's winning strike allowed City to keep pace with Chelsea and Manchester United at the top of the Premier League with 14 points from eight matches.