Goalscoring opportunities were at a premium in this encounter at The Den, with both teams struggling to find a way through the opposite defence, but it was Millwall who took their chance when it was presented to them.
Adam Smith picked up the ball on the right-hand side before playing it across the penalty area, where Feeney was able to fire into the back of the net from 12 yards with the help of a deflection.
Millwall, who reached the final of the competition in 2004, welcomed defender Smith back to the starting line-up for the visit of Preston, for whom Nicky Wroe recovered from a knee injury in time to claim a starting berth.
The hosts started brightly, with the first real chance of the match falling to Dany N'Guessan, whose shot at goal was blocked by Chris Robertson, allowing the visitors to clear the danger.
Kenny Jackett's men continued to enjoy the lion's share of possession in the opening 15 minutes, but struggled to carve out any meaningful goalscoring opportunities.
Darius Henderson went close to opening the scoring for Millwall on 20 minutes when his left-footed effort from 12 yards was deflected onto the Preston crossbar, but the visiting defence eventually cleared to safety.
Feeney broke the deadlock shortly after the half-hour mark when he met Smith's cross to finish powerfully, albeit with a touch of fortune.
The Lions continued to dominate play for the remainder of the half, but were unable to force their way through the Preston defence and extend their lead.
Preston's first-half chances were limited to a poor 42nd-minute strike by Wroe, who blazed his 12-yard effort over the crossbar.
Millwall continued to press after the break and a 52nd-minute strike by Henderson from inside the area forced Steve Simonsen into an impressive diving save.
North End tried to battle their way back into the match as it approached the 70-minute mark but, despite enjoying a greater share of possession, were unable to create any significant chances to claim an equaliser.
Smith picked up the only booking of the encounter on 67 minutes for a bad challenge on former Lions striker David Amoo.