The Cottagers were more than competitive in the first-half against Pep Guardiola’s side, but self-imploded after the break, conceding three times in 13 minutes.
While the first goal was the result of poor marking from a set-piece as John Stones opened the scoring, the two that followed were outright clangers, first as a defensive mix-up allowed Gabriel Jesus to double the lead and then as Tosin Adarabioyo was caught on the ball and gave away a penalty trying to recover.
“We tried to take the game to the best team in Europe and this division,” Parker said. “I thought we did do that.
“We conceded silly goals in the second half, which is disappointing but the players know that. I asked the team to be brave and show a way about us to try and assert ourselves on Man City. For large parts they did very well but it was some silly goals really.”
Fulham remain in the relegation zone only on goal difference, but have now played two games more than 17th-placed Brighton.
However, Parker is determined that Saturday’s defeat will do little to derail a survival bid that had been gathering momentum after last weekend’s win at Liverpool.
“There are massive positives,” he told BT Sport. “People may look at the way the goals were conceded but if you try to take a team on like Manchester City there are risks that come from that. We fell short. Overall I’m very pleased.
“[It’s a] big test now. Our season won’t be defined against a side like Man City. Now as always, we re-group, learn from the mistakes, take the positives and go again.”