Peter Crouch opened the scoring for the Potters with a stunning volley from around 25 yards before Yaya Toure equalised on 76 minutes with a long-range, deflected effort.
Roberto Mancini sent out his deputy as he was still seething from dropping points and Platt refused to believe mind games from the Italian and his Old Trafford adversary Sir Alex Ferguson will play a role in the title race.
He said: “The fact of the matter is Sir Alex and Roberto and whoever’s involved in it, because we’re in a title race, are going to have to answer questions.
“The be all and end all will be about 11 players going out on a pitch and getting results. It’s not about words, words won’t win the league.
“If we have more points than them at the end of the season people will perceive [Mancini’s] won the war of words, and if it’s the other way around people will perceive Sir Alex has won it. It’s actually inconsequential.”
The win sent Mancini’s men top of the table but only on goal difference, and a win or draw for the Red Devils at home to Fulham on Monday night would see City return to second place.
But former England international Platt refused to blame the Blues' squad for their failure to open up a gap at the top of the table.
“I think the issue of why we’re not pulling clear of the title race is that two teams have done particularly well,” he added.
“They’ve got the record of so many points at this stage of the season and we’re breaking those records.
“The fact that we’re not pulling away is because Manchester United have had a fantastic season.
“At the end of the day there’s 38 games, and to win it you have to make sure you have more points or a better goal difference than the other team.
“I don’t have to look at one performance because one performance doesn’t win you a league, it’s what you do over an entire season and I think we’ve all seen it over an entire season so far to say that we’re capable of winning the league.”
Manchester United could only manage a 1-1 draw at the Britannia Stadium and Platt insisted that the result will not necessarily prove detrimental to the Blues campaign.
He said: “I’m happy with the performance and Roberto’s happy with the performance of the entire season.
“As I said before it’s a difficult place to come to. People will say it’s two points lost but if we win the league by one point perhaps we’ll look back at this and say it was a good point.
“You won’t know until the end of the season.”
Platt also hailed former Liverpool striker Crouch's opener but insisted that it was a result of direct football.
“It’s a great goal,” Platt acknowledged. “It’s route one, it comes from the goalkeeper.
“It’s what you expect but as soon as it’s left his foot it’s on target and its going in the back of the goal.”
The game was a physical affair with a number of body checks and tough challenges, but the number of cards issued by referee Howard Webb was kept to a minimum.
“To be honest it’s going to difficult when you come here,” the City coach admitted.
“You know what to expect, you watch the game, it’s intense.
“You know it’s going to be difficult when you come here, you know they’re going to compete, they’re going to go for every ball and challenge for every ball.”
David Silva suffered a head injury when Stoke defender Dean Whitehead seemed to push his arm into the Spaniard's face when leaping for a tackle, although it looked accidental.
Platt added: “I’ve not seen the David Silva [challenge] - I know he’s got a cut in his ear but I haven’t seen it.
“I wouldn’t accuse the player of going for David Silva. He’s just competitive and that’s the way that they play.”