The low conversion efficiency of high-order harmonic generation (HHG) in gases is an insurmountable limitation for many applications, where a considerable photon flux is an instrumental prerequisite. We present a study of the HHG conversion efficiency dependence on the driving laser intensity and analyze the conditions for optimal phase-matching in a loose focusing configuration and long generation medium using a Ti:Sapphire laser. Moreover, by determination of the influence of plasma effects on the driving laser pulse, we observe a correlation between the HHG conversion efficiency and the blueshift of the fundamental pulse. The maximal HHG conversion efficiency is achieved just before the driving laser spectrum is considerably affected by the plasma. Similar behavior is observed in HHG for different noble gases. In this respect, the appearance of a plasma-induced spectral shift in the driving laser might serve as an indication of a substantial loss of HHG conversion efficiency. Consequently, our findings can be exploited to obtain essential information about the laser-plasma interaction process during HHG and can pave the way for a more convenient control of optimal HHG conditions.