Roy Hodgson fielded a strong side including England's World Cup captain Steven Gerrard as well as Jamie Carragher and Glen Johnson while Fabio Aurelio was named on the bench after re-signing for the club on Saturday.
Monchengladbach had arranged the match as part of their 110th anniversary celebrations at Borussia Park and the hosts made an early breakthrough through Karim Matmour in the eighth minute.
The Algerian took advantage of some poor play by Daniel Ayala inside the area and the defender was duly punished as Matmour produced a powerful finish.
Matmour was proving a real irritant for the Anfield club and came close to doubling his side's lead, with Liverpool having to wait until the 56th minute for their first real chance when Cole's low drive was parried, with the former Chelsea player withdrawn nine minutes later.
The hosts continued to threaten and, although David Amoo headed narrowly wide, Monchengladbach fully deserved their victory.