All is not lost for the Italian giants, who host the second leg of the last 16 clash at San Siro next week, but coach Roberto Mancini will surely be annoyed at the manner of their defeat, as Kevin De Bruyne struck twice for Wolfsburg.
Rodrigo Palacio gave Inter the lead in the fifth minute but they were pegged back before the break when Carrizo - one of two Inter inclusions - spilled a Naldo header.
While there were excuses for the goalkeeper on that occasion, namely a complete lack of marking, he was solely to blame for Wolfsburg's second as De Bruyne opened his account 27 minutes from time.
Given a backpass from substitute Nemanja Vidic, Carrizo completely fluffed a clearance, only finding Vieirinha on the right flank, and he stormed into the penalty area before cutting back for De Bruyne to do the rest.
Carrizo's night of misery continued when he was wrong-footed by De Bruyne's 75th-minute free-kick, which, despite being an effort he really should have saved, crept into the right corner.
The visitors took the lead when their intense press reaped an early reward.
Andre Schurrle, under serious pressure from Danilo D'Ambrosio, volleyed an errant pass at Mauro Icardi and the Inter man cleverly slid in Palacio.
Having been put through on goal, the forward kept his cool to slot past Diego Benaglio and delight the travelling fans.
Wolfsburg, who left themselves open on the break, saw Schurrle waste a pair of chances before Carrizo made an excellent reaction save to keep out Daniel Caligiuri's near-post header.
Carrizo should have done better from the resultant corner, though, as Wolfsburg levelled proceedings in the 28th minute.
De Bruyne's ball fell to an unmarked Naldo, and the central defender's fierce header from nine yards was too hot to handle for Carrizo, who could only help it into the roof of the net.
Buoyed by their goal, Wolfsburg ended the half stronger, with right-back Vieirinha drawing a good save from Carrizo after a mazy run two minutes before the break.
Caliguiri and Ricardo Rodriguez went close with efforts from distance after the resumption as Wolfsburg picked up where they left off, before Palacio spurned a great chance in the 57th minute.
Davide Santon played in the Argentinian, who took a touch before smashing an effort into the side netting.
Inter introduced Vidic in a bid to stem Wolfsburg's flow but the change indirectly led to another goal, as his pass to Carrizo sparked a scramble that ended when De Bruyne turned Vierinha's ball into the bottom-left corner.
And the Belgian did not have long to wait for a second goal, curling a 20-yard free-kick past Carrizo to open up a two-goal lead for Wolfsburg, which remained after both Icardi and De Bruyne wasted late chances.
