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.
"We're happy with the result and performance," Platt, the first-team coach, said. "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."
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."
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 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."