City's Premier League title hopes appear all-but over, but with a six-point advantage over third-placed Arsenal, a runners-up spot looks firmly within their grasp.
City are back in Premier League action on Wednesday night, three days after their semi-final win over Chelsea, as they host relegation-threatened Wigan in a cup final dress rehearsal at the Etihad.
Platt said: "Rather than dramatising the situation, it is about finishing the season as strongly as we can do.
"You would probably put money on us finishing second now and hopefully we will win the FA Cup. But we still have to play a good team and anything can happen in the final.
"We have our own expectations and our own expectations are very high."
Some pundits believe that since conceding defeat to United in the Premier League title race - City currently trail their rivals by 15 points - they have started playing without pressure.
But Platt disagrees, adding: "I don't think it is a case of that, the pressure is still on to win football games."