How does one respond to 3.d4 after playing the Sicilian? I was black in this game, and white went ahead and played 3.d4 even though I clearly had it guarded, however once played, white now has the queen as an additional defender, and the queen was able to rest on d4 with no threat from black. In response I played 

[FEN ""]
1.e4 c5 2.Nf3 Nc6 3.d4 cxd4 4.Nxd4 Nxd4 5.Qxd4 Qa5+ 6.Nc3 e5


I went on to lose this game, but I feel like this was the deciding factor. I really don't feel like 5...Qa5+ was the best reply, even if white was to reply with 6.Bd2 I could still reply with 6..e5 and propose a queen sac, which after black wouldn't be in as bad a position.

[FEN ""]
1.e4 c5 2.Nf3 Nc6 3.d4 cxd4 4.Nxd4 Nxd4 5.Qxd4 Qa5+ 6.Bd2 e5 7.Bxa5 exd4


So, my question is: Is black's best response to 3.d4 after playing the Sicilian 3...cxd4? Also, if so, was there a blunder somewhere by black, or could a better move have been played elsewhere?
3...cxd4 is indeed basically forced. Perhaps the single biggest idea of the Sicilian is to exchange your c-pawn for White's d-pawn, leaving you with more pawns in the center. So go ahead and do it!

However, 4...Nxd4 is a mistake, leaving White with much better development after the trade.

Some common 4th moves for Black after 1.e4 c5 2.Nf3 Nc6 3.d4 cxd4 4.Nxd4 are 4...Nf6 (attacking the e4 pawn), 4...e6 (preparing to develop the dark-squared bishop and/or play ...d5), and 4...g6 (planning to develop the dark-squared bishop to g7).