With their London-born manager Pascal Jansen also making changes, Ferencváros substitute Fortune Bassey shot low across the face of goal, before Makreckis saw his cross-shot cannon back off the underside of the crossbar, while West Ham probed for a late equaliser.
And that probing paid off with seconds to play when a free-kick was cleared as far as Andy Irving. The Scot crossed from the right and Nayef Aguerd volleyed accurately into the net with his left foot to secure a draw!
Next up for Lopetegui and his new charges will be a much shorter trip to Chigwell Construction Stadium to face National League side Dagenham & Redbridge on Saturday at 3pm BST.
Ferencváros: A.Varga, Cissé, Raul Gustavo, Ramírez, Abu Fani, Maïga, Makreckis, Kehinde, Traoré, Owusu, Pešić
Subs: Szécsi (GK), Radnóti (GK), Knoester, Ben Romdhane, Ćivić, Zachariassen, Botka, Gruber, Bassey, Aaneba, Katona, Rommens, Kady, Tóth
Goals: Kwabena 23, Pešić 38
Booked: Maïga
West Ham United: Fabiański (Foderingham HT), Kodua (Marshall 60), Mavropanos (Zouma HT), Kilman (Aguerd HT), Cresswell (Emerson HT), Orford (Earthy HT), Potts (Moore 68), Ward-Prowse (Irving HT), Guilherme (Kelly 54), Kudus (Casey HT), Cornet (Ings HT)
Subs not used: Terry (GK), Herrick (GK), Robinson
Goals: Ings 48, Aguerd 90