North End held the Blades to a 1-1 draw at Deepdale last Friday before losing Monday's decisive second leg 1-0 at Bramall Lane.
Kevin Blackwell's men were largely dominant in both encounters and Mellor acknowledged they were worthy victors.
The former Liverpool striker told the club's official website: "We probably only threatened in the last 15 minutes of the whole tie.
"On the days they were the better side and dominated the games, which was disappointing."
Source: Team_Talk