City dominated from the outset at the Etihad Stadium and although they were made to wait until the 43rd minute for Pablo Zabaleta's opener, the result was rarely in doubt.
Edin Dzeko and Sergio Aguero, from the penalty spot, wrapped up the routine success after the break.
Platt, the first-team coach, said: "We're happy with the result and performance.
"I think the goal just before half-time was more than deserved.
"But it doesn't make the second half any easier - you've still got to go out and play, but it just settles you down a bit without the clock running against you.
"They have shown all season it is hard to score goals against them."
With leaders Manchester United winning at Wigan, City remain seven points behind their rivals at the top of the table.
Platt said: "We have just got to continue to win football matches.
"We have been producing chances in games over the last month to six weeks.
"We lamented a little bit at Sunderland the chances we produced without scoring enough goals. Fortunately we are getting our ratios up."
The match was City's last with Yaya Toure before their midfield talisman links up with Ivory Coast for the African Nations Cup along with brother Kolo and striker Abdul Razak.
Yaya Toure's absence was keenly felt during last season's tournament but Platt says the team must cope.
He said: "It is irrelevant whether Yaya disappears or not. The challenge is to keep winning football matches.
"We have a squad of players that we will have to choose 11 from.
"Whichever 11 we put on the park we would expect to go and take the points."
Stoke provided little threat during the game and manager Tony Pulis made no excuses for their lacklustre display.
Pulis said: "I've no complaints, they were the better team.
"Someone has just asked me what the difference was - I said about £220million.
"For us to come here we have to bring our 'A' game and City have to be off it.
"That wasn't the case today [Tuesday] but you have to sometimes open your eyes and look at the reality of everything. They have got a bit of a head start on clubs like us.
"I don't know whether it was because it was the fourth game in the holiday period and we didn't bring our 'A' game - but I am not going to criticise the players.
"They still worked their socks off, they worked very hard. City were the better team.
"You hold your hands up and dust yourself down. We have got a tough game now at Crystal Palace."
The Potters had been unbeaten in 10 matches prior to the game but Pulis will no consider strengthening during the January transfer window to ensure a strong finish.
He said: "We would like to do some business but we have to wheel and deal as well. We have to get a few out.
"If we can do that we will try to get a couple in. I think the squad needs a little bit of fresh blood but we have to generate it. We can't go out and spend the money.
"If we get room and space and the players are available, then we will do it."