  The evidence for particle acceleration in supernova shells comes from
electrons whose synchrotron emission is observed in radio and X-rays. Recent
observations by the HESS instrument reveal that supernova remnants also emit
TeV gamma-rays; long awaited experimental evidence that supernova remnants can
accelerate cosmic rays up to the ``knee'' energies. Still, uncertainty exists
whether these gamma-rays are produced by electrons via inverse Compton
scattering or by protons via neutral pion decay. The multi-wavelength spectra
of supernova remnants can be fitted with both mechanisms, although a preference
is often given to neutral pion decay due to the spectral shape at very high
energies. A recent study of the interstellar radiation field indicates that its
energy density, especially in the inner Galaxy, is higher than previously
thought. In this paper we evaluate the effect of the interstellar radiation
field on the inverse Compton emission of electrons accelerated in a supernova
remnant located at different distances from the Galactic Centre. We show that
contribution of optical and infra-red photons to the inverse Compton emission
may exceed the contribution of cosmic microwave background and in some cases
broaden the resulted gamma-ray spectrum. Additionally, we show that if a
supernova remnant is located close to the Galactic Centre its gamma-ray
spectrum will exhibit a ``universal'' cutoff at very high energies due to the
Klein-Nishina effect and not due to the cut-off of the electron spectrum. As an
example, we apply our calculations to the supernova remnants RX J1713.7-3946
and G0.9+0.1 recently observed by HESS.
