Using the latest upper limits on the 21-cm power spectrum at z approximate to 9.1 from the Low Frequency Array (LOFAR), we explore the regions of parameter space which are inconsistent with the data. We use 21CMMC, a Monte Carlo Markov chain sampler of 21CMFAST which directly forward models the three dimensional (3D) cosmic 21-cm signal in a fully Bayesian framework. We use the astrophysical parametrization from 21CMFAST, which includes mass-dependent star formation rates and ionizing escape fractions as well as soft-band X-ray luminosities to place limits on the properties of the high-z galaxies. Further, we connect the disfavoured regions of parameter space with existing observational constraints on the Epoch of Reionization such as ultra-violet (UV) luminosity functions, background UV photoionization rate, intergalactic medium (IGM) neutral fraction, and the electron scattering optical depth. We find that all models exceeding the 21-cm signal limits set by LOFAR at z approximate to 9.1 are excluded at greater than or similar to 2 sigma by other probes. Finally, we place limits on the IGM spin temperature from LOFAR, disfavouring at 95 per cent confidence spin temperatures below similar to 2.6 K across an IGM neutral fraction range of 0.15 less than or similar to (x) over bar (HI) less than or similar to 0.6. Note, these limits are only obtained from 141 h of data in a single redshift bin. With tighter upper limits, across multiple redshift bins expected in the near future from LOFAR, more viable models will be ruled out. Our approach demonstrates the potential of forward modelling tools such as 21CMMC in combining 21-cm observations with other high-z probes to constrain the astrophysics of galaxies.