Foden provided two assists before half-time, and Cherki came off the bench to set up Savinho's third in the 84th minute — a run and pass of genuine top-level quality. The result moves City to 79 points, two behind Arsenal, with goal difference now tilted in their favour.
Speaking to BBC Match of the Day, Guardiola was unstinting in his appreciation of Foden's contribution.
"Phil, we know his qualities. I appreciate him a lot. Incredible runner and fighter. In the final third, an incredible spark. I was really pleased with that."
"These type of games, they play the low block — it is the talent for the wingers, like Phil in the first goal. These types of games, the quality makes the difference. And Phil is full of it in his body. I am beyond happy and satisfied."
Cherki, signed from Lyon in January, drew equal praise after his impact from the bench.
"Rayan has incredible quality coming from the bench and making an impact. Kovacic and him make an impact."
On the night's work more broadly, Guardiola acknowledged Palace's defensive organisation made life difficult before City's quality told.
"We had to work, but Crystal Palace worked harder. We were better. A tough team to break down because they defended incredibly well."
"I trust all of them a lot. Sometimes it is for the way we play, sometimes it is shape. Omar is always there, the work ethic, the goals. We played really, really good. I know their transitions are top, the set pieces. It is difficult because they defend really well in the low block. It is tough but we did it with patience. We made the game we should play."
On the title race, Guardiola was brief and clear-eyed.
"Depends on them. If they win two games — nothing to do, nothing to talk. All we can be is in there just in case. The last two games are tough."
Arsenal host Burnley on Saturday before travelling to Everton on the final day. City face a testing run-in of their own — Brighton and Bournemouth — but must first navigate Saturday's FA Cup final, where Guardiola was direct about the stakes.
"The FA Cup, incredible respect. We lost the last two times because we were not good enough. We are going to go there to win. We have to be ready physically and mentally against a team who are not in the best season, but the quality is there. Of course, they will do their best, and we have to do our best to try to win."
He was equally brief on turning around from a crucial league night to an Wembley final inside 72 hours.
"All we can do is go to sleep as quickly as possible and prepare for the FA Cup. That is what we have to do."
City's squad has been bolstered by the return of Josko Gvardiol, who made his first appearance in some time on Wednesday, and the depth across the group gave Guardiola the luxury of significant rotation while still producing three goals and a clean sheet.