It may have been five years since Anfield had played host to a Champions League night, but it was a familiar story, with Gerrard the hero again after the Bulgarians had cancelled out Mario Balotelli's opener.
The £16m signing from AC Milan opened his Liverpool account with a smart outside-of-the-boot finish, but first goals do not come any better than Enner Valencia's maiden strike for the Hammers.
Carroll cost the Londoners a club-record £16m when they bought him from Liverpool in 2013, but will miss the visit of his former club as he continues to recover from ankle ligament damage.
Kevin Nolan and Joey O'Brien are also long-term absentees and, while Matt Jarvis should be fit after a muscle strain, Allardyce may not have room for the winger, even if he switches back to a 4-3-3 system.
Having both enjoyed cameos as substitutes at the KC Stadium, Arsenal loanee Carl Jenkinson and former Gunners midfielder Alex Song could make their first Hammers starts, at the expense of Guy Demel and Diafra Sakho.
Rodgers has dropped his diamond formation since losing Daniel Sturridge to injury, but may turn back to it so that Raheem Sterling can have a greater influence on proceedings in the role behind the strikers.
Sturridge, Glen Johnson, Jon Flanagan, Joe Allen and Emre Can are all ruled out of the trip to Upton Park and it may also come too soon for Skrtel, who resumed training this week after a spell on the sidelines.
Liverpool, eighth in the table, have lost just two of their last 23 matches against the Hammers, who are 13th.
West Ham: DLDWL
Possible starting lineups
West Ham: Adrian; Jenkinson, Reid, Tomkins, Cresswell; Kouyate, Song, Noble; Downing, Zarate, Valencia
Liverpool: Mignolet; Manquillo, Lovren, Sakho, Moreno; Gerrard, Henderson, Coutinho, Sterling; Balotelli, Lambert
Sports Mole says: 1-2