Sergio Aguero levelled for the City in the second period, but they could not force the equaliser. Roberto Mancini's side can still qualify with two wins, but it will depend on other results.
Read how it all unfolded in Sports Mole's minute-by-minute live commentary below.
Manchester City: Hart; Zabaleta, Kompany, Nastasic, Clichy; Garcia, Barry, Toure; Nasri, Aguero, Tevez
Ajax: Vermeer; Van Rhijn, Alderweireld, Moisander, Blind; Schone, Poulsen, De Jong; Boerrigter, Eriksen, Babel