Nketiah’s 97th-minute effort came with Arsenal defender Rob Holding stood in an offside position to the side of Fulham goalkeeper Alphonse Areola, who had saved Dani Ceballos’ initial shot.
However, as Holding did not touch the ball he was deemed not to be interfering with play as Gunners forward Nketiah tapped in.
It delivered a major blow to the Cottagers, who led through Josh Maja’s second-half penalty and looked on course to gain a valuable three points in their battle against relegation.
That was a real painful one, Parker said. I don’t know how the goal stood. I don’t understand it. I am a little bit confused but we are all confused of late.
We all scratch our heads a bit, people who have played the game for a long time. Whether he [Holding] attempts to go for the ball or not the ramifications of his position affect my goalkeeper.
What is factual for us is we’ve come to another place and the difference between one point and three points is a decision with the last kick of the game.
The result leaves Fulham six points from safety but they have played one game more than Burnley – the side directly above them – and two more games than Brighton in 16th.
On-loan Bordeaux forward Maja opened the scoring with Fulham’s only effort on target after Mario Lemina was fouled by Arsenal’s Brazilian defender Gabriel.
However, in a game of few clear-cut chances Arsenal, who remain ninth, merited their point.
Mikel Arteta’s side had Ceballos’ first-half goal disallowed after Bukayo Saka had strayed fractionally offside, while Gabriel Martinelli also found the back of the visitors’ net after the whistle had gone for offside against Emile Smith Rowe.
Substitute Nicolas Pepe and Saka also both went close to levelling the score before Nketiah’s late intervention.
After dismantling Slavia Prague in the Europa League on Thursday, Arsenal did little to dispel the feeling of unpredictability that surrounds them as they faced a team battling the drop.
On paper, Arteta would have expected his side to dispatch their struggling opponents with few difficulties.
But their up-tempo start, which saw Martinelli twice go close to scoring, soon fizzled out.
That allowed the visitors to gain a foothold in the match, although VAR contributed to Arsenal’s failure to break the deadlock with Ceballos seeing a header ruled out after Saka was judged to be centimetres offside in the build-up.
To their credit, Arsenal persevered after going behind despite seeing Alexandre Lacazette limp off with 20 minutes left.
And a late siege saw Nketiah, Saka, Gabriel and Martinelli all have efforts on goal before their dominance finally told.