It is the eighth successive year City have got through their group.
Guardiola’s most pressing issue is now kick-starting their Premier League campaign after a stuttering opening which has seen them win just three of eight games.
“We came here to get to the last 16 and we are there again, another year,” said manager Guardiola.
“Now we recover as quick as possible and start focusing on the Premier League.”
In keeping with a number of their games this season, City again failed to make the most of their chances.
They racked up 22 shots but Foden’s sweet 36th-minute strike, from a clever Raheem Sterling backheel at the end of a flowing move, was all they had to show for their efforts.
Yet with Olympiacos offering little in attack – they failed to register a single shot on target – the visitors never looked likely to slip up.
Guardiola, who rested Kevin De Bruyne, is confident the goals will come “sooner or later”.
“We were much more aggressive,” said the Catalan, whose side host Burnley on Saturday. “Everyone was so committed and we attacked with more desire to shoot, to score.
“Unfortunately we could only score one goal but the team is alive. We made an incredible group stage. That’s 12 points so we are already qualified and are going to try to finish first.”
Olympiacos complained after the game that Foden’s goal should not have been allowed to stand, believing Mohamed Drager to have been fouled prior to City’s sweeping move upfield.
Club owner Vangelis Marinakis said at a press conference: “In the goal of Manchester a clear foul was made, an elbow to Drager. It is very easy for the referees to see it in the VAR and inform the referee if he has not seen it himself.
“It is not nice when the players give everything on the field and can get a good result but the refereeing is unfair to us once again.”
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