Celtic suffered a demoralising defeat at home to a weakened Sparta Prague side on Thursday night in the Europa League.
The defeat wiped away the positivity they gained from getting a point at Lille last week and beating Aberdeen in the Scottish Cup semi-final at Hampden Park on Sunday.
The defeat to Sparta Prague was one more bad result added to a string of poor Celtic performances in Europe over the last two years and Rough feels it should not be acceptable to the Bhoys fans.
There are suggestions that Lennon could soon lose his job if results do not improve soon and Rough conceded that could be the case despite the Celtic manager insisting that he has a good relationship with the club hierarchy.
The former Bhoy said on PLZ Soccer: “It is just not acceptable to the Celtic fans.
“They have a standard, particularly in European football, but it shows how much Celtic have dropped over the last two or three years from being a Champions League team to not even a Europa League side with a result like that.
“A lot of questions need to be answered.
“Neil keeps saying he has a good relationship with the owners and it has to be a pretty strong one for the next couple of weeks.”
Celtic will travel to Fir Park to take on Motherwell this afternoon in a Scottish Premiership clash.
