Goals by Leon Osman and Nikica Jelavic sealed victory for the Toffees, who were forced to play the last half an hour with 10 men after Steven Pienaar was sent off for a second bookable offence.
First-team coach Platt admitted that his side were far from their best, but claimed a decision from Lee Probert on a Marouane Fellaini handball in the area near the end might have changed the game for City if it had been given as a penalty instead.
“From where I was live, I didn't know whether it was in the area or not. He's just played it back to me. It's not even on the line, it's three yards inside. People can draw their own conclusions from that," he told Sky Sports.
“Perhaps our performance didn't deserve it but that's by the by. Maybe we could have got more out of the game if decisions had gone for us.”
Manchester United remain 12 points head of City, and Platt seemed resigned to the title going to Old Trafford this season, but insists the team still has a job to do.
He said: “Nobody has been chasing from the rooftops saying we're chasing Manchester United down, they've got a significant points advantage over us, even if we won the game today it still would have been 12 points, you'd expect them to win at home today anyway.
“But we've still got an obligation between now and the end of the season, whether it's mathematically possible, which it is at this time, or not, to go out, be professional and win football matches”
David Moyes, meanwhile, was understandably buoyant following the victory that he felt reminded the club's fans of the team's quality after being dumped out of the FA Cup last time out by Wigan.
“We were very good, and we have been for just about the majority of the season," he said. “We’ve had one or two dips here and there, but that was certainly more like us today.
“I never thought that Everton were away; I thought that we had a bad performance which we’ve been reminded of by the supporters, and rightly so, we didn’t play well enough. But I think we’ve just reminded them that they’re actually supporting a really good team.
“We’re playing the champions of England at this present time, they’re second in the league, we’re not going to always be able to out pass them, outplay them; but we had to make sure that when they did have the chance to do that, when it went to 10 men, that we’re hard to beat and we did so.”
Moyes, however, was also unimpressed with some of the decisions during the match and felt Steven Pienaar, who was sent off in the second half, did not deserve to be red carded.
The Scotsman added: “I thought we played really well in the first half, I thought we had a goal, which was wrongly disallowed, and I certainly don’t think it was a sending off.”