What should I do if I cannot pray exactly towards the Qibla due to lack of space in a tiny room?
I can perform the prayer, if the 'owner' is not there at that moment, in a room where I do have enough space but still cannot perform it comfortably. This is because first of all I have to put away all kinds of things and every time I get up from my Sujud the carpet is pushed away. This all makes me lose my concentration in the prayer, which I firstly had when praying in my room with a not 100% correct qibla.
Bismihi ta'ala
It is necessary to find the correct direction of the Qiblah, and aim at praying towards it. Having a tiny room would not be a good enough excuse to not pray towards the Qiblah. You are able to push aside some furniture, or find alternative places to pray. If you are within the overall right direction of the Qiblah, that would suffice.
And Allah knows best.