At the distance of 99-116 pc, HD141569A is one of the nearest HerbigAe stars that is surrounded by a tenuous disk, probably in transition between a massive primordial disk and a debris disk. We observed the fine-structure lines of OI at 63 and 145 micron and the CII line at 157 micron with the PACS instrument onboard the Herschel Space Telescope as part of the open-time large programme GASPS. We complemented the atomic line observations with archival Spitzer spectroscopic and photometric continuum data, a ground-based VLT-VISIR image at 8.6 micron, and 12CO fundamental ro-vibrational and pure rotational J=3-2 observations. We simultaneously modeled the continuum emission and the line fluxes with the Monte Carlo radiative transfer code MCFOST and the thermo-chemical code ProDiMo to derive the disk gas- and dust properties assuming no dust settling. The models suggest that the oxygen lines are emitted from the inner disk around HD141569A, whereas the [CII] line emission is more extended. The CO submillimeter flux is emitted mostly by the outer disk. Simultaneous modeling of the photometric and line data using a realistic disk structure suggests a dust mass derived from grains with a radius smaller than 1 mm of 2.1E-7 MSun and from grains with a radius of up to 1 cm of 4.9E-6 MSun. We constrained the polycyclic aromatic hydrocarbons (PAH) mass to be between 2E-11 and 1..4E-10 MSun assuming circumcircumcoronene (C150H30) as the representative PAH. The associated PAH abundance relative to hydrogen is lower than those found in the interstellar medium (3E-7) by two to three orders of magnitude. The disk around HD141569A is less massive in gas (2.5 to 4.9E-4 MSun or 67 to 164 MEarth) and has a flat opening angle (<10%). [abridged]