The 19-year-old made his maiden first-team appearance in a 1-1 draw at Elland Road.
The 19-year-old filled in for first-choice Marco Silvestri against Queens Park Rangers, after the Italian was sent off in Saturday's defeat to Rotherham United.
And he was three minutes away from marking his Elland Road bow with a clean sheet, with Tjaronn Chery scoring QPR's equaliser from the penalty spot.
Silvestri returns to contention for Saturday's tip to Burnley and is expected to reclaim his place between the sticks, though speaking to BBC West Yorkshire Sport, Peacock-Farrell said he hopes to feature again soon - starting at Turf Moor.
"No I wouldn’t (like to give up my shirt)," admitted the Darlington-born shot-stopper. "But whoever plays on Saturday that’s down to the gaffer and the coaching staff."
He added: "I’d like to play some more games (between now and the end of the season). No targets - I’ll see how it goes."
Asked if it would be weird dropping down to the bench after this, Peacock-Farrell replied: "Possibly. I’ve done it throughout the season. Every goalkeeper wants to play, whether you’re 19, 25 or 35 - but that’s up to the gaffer."
Leeds boss Steve Evans told the Yorkshire Evening Post before the game that he wouldn't automatically replace Peacock-Farrell with Silvestri on Saturday, adding that the youngster has a big future ahead of him and this will be the first of many Whites appearances.