The 22-year-old striker told reporters he has asked to return to Stamford Bridge, ahead of seeking another loan move in January.
Bamford blasted a point-blank effort straight at grateful Swansea goalkeeper Lukasz Fabianski when he should have buried the winning goal at Selhurst Park.
His goalless nine-game stint with the Eagles now looks at an end, despite manager Alan Pardew saying Palace were yet to talk to Chelsea on Bamford’s future.
“Strikers will always tell you they need five games,” said Pardew of Bamford’s form.
“Patrick, nine times out of 10, would have buried that and we’d have got three points. But I can’t be disappointed. Maybe he just needs that goal to give him that spark that strikers need.”
When asked if Chelsea would recall Bamford in January, Pardew added: “I think it’s a conversation we’ll have to have with Chelsea for sure, but we haven’t had it yet.”
Eagles boss Pardew said referee Neil Swarbrick’s booking of Yohan Cabaye was a “terrible decision”.
Midfielder Cabaye will now miss Palace’s home Premier League clash with Chelsea on Sunday, after his fifth yellow card of the campaign.
Pardew said he hopes missing strikers Dwight Gayle, Bakary Sakho and Conor Wickham can quickly find fitness, to boost his side’s stretched resources.
“Swansea got their shape very, very quickly and the game never really opened up. But we’ve got 31 points after 18 games: wow. That’s fantastic for us. Now we’ve got to hope some of our strikers come back to us. You could tell it was our second game in three days.
“We lacked a bit of imagination and flair. The discipline was spot-on, but that little spark, that little edge, we didn’t have that today. We’ll certainly miss Yohan (Cabaye) against Chelsea, because he’s a great player for us. So we’ll have to manage without him,” he said.
Swansea’s caretaker boss Alan Curtis said he has still not had any direction from club chiefs over a long-term replacement for former manager Garry Monk.
Swansea have now accrued two draws, a win and a defeat from Curtis’s temporary stint, and the man currently in the hot seat expects to be in the dugout for Saturday’s trip to Manchester United.
“Nobody’s said anything to me, we’re just carrying on as normal,” said Curtis of the club’s ongoing managerial search.
“And now we’re just looking towards next weekend. The club are in the process of I think interviewing people, or certainly looking at potential candidates.
“There is a need to sign somebody slightly different.”
Hennessey, Ward, Dann, Hangeland, Souare, Jedinak, McArthur (Mutch 75), Zaha, Cabaye, Puncheon (Lee 71), Chamakh (Bamford 46).
Fabianski, Naughton, Amat (Bartley 77), Williams, Taylor, Shelvey (Ki 56), Cork, Grimes, Emnes (Sigurdsson 56), Gomis, Barrow.