Brendan Rodgers' Celtic side picked up a 2-1 win in the Europa League last night.
Mulumbu was brought on by Rodgers for the last 10 minutes of the contest, as Celtic looked to see out an important victory.
The experienced midfielder was supposed to tighten things up for Celtic and limit the chances that Red Bull Leipzig got.
However, he put in an error strewn display, and was fortunate not to be at fault for Celtic letting their lead slip.
Mulumbu presented Leipzig with a great opportunity which Kevin Kampl wasted from close range.
In the end Celtic held out to win 2-1 and keep their hopes of progressing in the Europa League alive.
But Sutton said: “Mulumbu, since he’s come on, he’s had a nightmare. He hasn’t got the pace of the game at all.”
Mulumbu has only just returned from injury for Celtic, but his performance is unlikely to have increased his chances of starting in future weeks.
Mulumbu has found game-time difficult to come by since moving to Parkhead, and Rodgers may think twice about starting him now.