City kept up their challenge at the summit with a 2-0 win over Fulham on Saturday, a result which helped cut the gap at the top to five points following United's draw with Tottenham a day later.
But Roberto Mancini's right-hand man was eager to underline his team's status as underdogs in the race for top spot.
"It's not over, we can make it up, it's not insurmountable by any stretch of the imagination," Platt told reporters. "But equally, it's theirs to lose."
The former England international went on to admit that the reigning champions were not at their best against the Cottagers, but praised their ability to grind out a result.
"Did we perform brilliantly well? No, I don't think so. The second half was much better and it was assured, it was a complete performance in many ways," he added.
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"We played Stoke here the other week and a lot was made of the fact Stoke didn't do anything but we restricted them to very few things and we've done that again.
"The next game is another game and you've just got to get on with it. Go into it and win it. You can't really say our best form is yet to come but I think we are playing well and we've got to make sure that continues."
During his playing days, Platt helped Arsenal overturn a 13-point deficit to beat Manchester United to Premier League glory, but the 46-year-old claimed the two situations were not similar.
"It's slightly different in the fact that back then, I think we lost three out of four games around Christmas time and we didn't go into games after that thinking, 'What we've got to do to win the league is win the next 13 games or something'," he said.
"It just happens and it's probably about six games before the end before you think you've got a sniff of a chance. Every season is different and people like to have headlines like, 'we're coming to get you', 'we're doing this', 'we're doing that'. But the fact of the matter is they're clear at this moment in time."
The Chadderton-born coach also expressed his belief that City have begun to pick up consistency following their defeat to United on December 9.
"I thought we were a bit stop-start at the beginning of the season but even going into the United game I thought, at the beginning of December, we started to play and be more consistent," he continued.
"People say we didn't go on to win games by four or five, or like the six we got at United [last season] but I thought we were playing consistently well. Each department of the team was playing, it was flowing.
"Even though we got beat by United I think we performed well in that game too. The other blip we've had was at Sunderland [losing 1-0] but even that one was a strange game when you look at it. I think we would win that game nine times out of 10 with the chances we've created."