The 25-year-old set a world record time of 3:50.15 to triumph in front of a huge crowd at the Olympic Stadium, sparking questions about whether he could run in the Olympics.
He said: 'I am still young and maybe I am still aiming high, aiming to the sky and if I fall down I fall from the clouds.'
Ethiopian Wondiye Fikre Indelbu was on Tarbei's shoulder about 150m from the finish line but ended with silver as the Kenyan held him off.
Tarbei said: 'I was very careful about him because they are tough guys, so I was very steady. I just go and go and go and conquer the world.'
I just go and go and go and conquer the world.Abraham Tarbei
Asked if he would like to emulate South Africa's Oscar Pistorius, who ran at the Olympic Games, Tarbei said: 'Exactly, that is my prayer and I will go back and work for this to make sure I am in the Olympic and Paralympic Games in Rio.'
He dedicated the medal to his fellow Kenyans, his team-mates, wife and daughter, adding: 'I am very grateful. I thank God for this. It was not my achievement alone.
'I have said before it was my ambition to come here and to break our record which has come today, so I am very happy, very thankful.'