The former Chelsea man, who was sent off in his Reds debut against Arsenal on Saturday, was unable to convert a 52nd minute penalty which would have given his side a comfortable two-goal lead at Anfield.
But thankfully for Cole, he was earlier involved in giving Liverpool their opener which they were able to hang onto, giving them a slender advantage going into the second leg.
In injury time of the first half, Cole sent a sublime pass through to Ryan Babel, who acted as a loan striker for much of the contest, and the Dutchman slotted home with precision before being hooked at half-time.
Roy Hodgson's men should have won by a greater margin but nonetheless, a win of any kind will give the side confidence.
Danish midfielder Christian Poulsen made his Anfield debut whilst skipper Steven Gerrard sat out proceedings.