The choice of intro pack is likely what hurt you the most. The Deckbuilder's Toolkit, in it's current incarnation, comes with 2 pack of 2011 Core Set, 1 pack of Mirrodin Beseiged, and 1 pack of Scars of Mirrodin (I believe).
The semi-random cards are not from the Scars of Mirrodin block, which is the only block to contain the Infect ability. Basically, of the 285 cards in the Toolkit, only a few of them could have had Infect (only cards in the Scars pack and the Besieged pack could have had infect cards).
If you're looking to pick up a bunch of cards with Infect, your best bet is to buy packs from either Scars of Mirrodin, Mirrodin Besieged, or New Phyrexia, look through the binders or case for cool cards with Infect, or buy one of the two Infect based Event Decks.