Why did not white win?

Why did not white win?
Black queen just kept circling white king waiting for repetition move (draw) or a blunder; getting forked (king-rock).

How can white manage to get a queen?

He probably can't, tbh.

I don't see where he can.

1 Ke3 Qb3+ 2 Rd3 is the only apparent try.  If either the e7 Pawn or the c7 Pawn is captured then the other one queens.  You may eventually have to get your Rook to c1 or e1 and your King on h1 before you can queen.

One reason why White didn't win. 

Did you mean why didn't Black win?

No. 1.Ke3 Qe6+ then QxR

Granted.

1 Kf1 Qa1+ (1 ... Qb1+ 2 Ke2 Qb5+ 3 Rd2) 2 Ke2 Qe5+

3 Kd3/Kf1 Qb5+

3 Kd1 Qa1+ 4 Kd2 Qb2+

3 Kd2 Qb2+ 4 Kd1 Qb3+

3 Kf2 Qb2+ 4 Kg3 Qe5+

Looks difficult for White to get away cleanly.

Ok, so I dont have to feel stupid for loosing.

Yes. I just overlooked Rd3 (I assume you meant). After Kf1 I should have played:

The upshot is Black has at least a draw by repetition.

Probably not, but we only showed at least a draw for Black so far, not necessarily a win. (You asked why White didn't win, not why White lost.)

After 1 Kf1 Qc4+ 2 Kg1?? Qc5+ 3 Kf1 Qb5+ picks up the Rook, stops the Pawns and wins.

1 Kf1 Qc4+ 2 Ke1 Qe5+ 3 Kd2 goes into earlier reviewed lines.

Talking a bit at cross purposes I think.

My aim in both diagrams I posted is not to show best play by Black, rather to answer OP's question by showing that Black has a line against which White can't win.

Obviously in the second diagram White would not in reality walk into the corner and get himself mated. But the argument shows that if he doesn't Black can at least draw by repetition.

The question marks you append to 2. Kg1 are amply justified. The move is shown just to make the argument complete. Similarly 3...Qb5 is obviously superior to 3...Qc4 in response to 3.Kf1, but either is sufficient to show White can't win in the 1.Kf1 line. 

Of course Black could get ambitious and waive the repetitions.  It may be he can force a win, but that's a different question.