The NFL announced the league's compensatory picks in a press release last night, and the result for Carolina is disappointing -- not a single selection. You can find the league's press release here, which includes a full listing of the players lost and gained, resulting in the compensatory selections.
In order to gain a compensatory pick, a team needs to have a net loss of players in free agency. Once there is a net loss, the round value is established by measuring the disparity between incoming, and outgoing salaries. For example, when the Panthers lost Julius Peppers he signed a mammoth deal with Chicago, and Carolina did not sign a player of equivalent value -- they were awarded a third round selection, the highest the compensatory process offers.
Initially it was believed the Panthers could get at least one selection for the loss of Dan Connor, but looking back at 2012 free agency, it's accurate.
Lost (Three players total)
OG Mackenzy Bernardeau (Dallas)
LB Dan Connor (Dallas)
WR Legedu Naanee (Miami)
Gained (Five players total)
FS Haruki Nakamura (Baltimore)
OG Mike Pollak (Indianapolis)
P Nick Harris (Jacksonville)
S Reggie Smith (San Francisco)
FB Mike Tolbert (San Diego)
There you have it. The Panthers gained two more players than they lost, so no compensatory picks. It's a shame, but as John Fox says "It is what it is".