The Hoops won a third straight Scottish title last week to continue their dominance on the Scottish game since Old Firm rivals Rangers were demoted to the lower leagues for tax breaches.
McCoist was quick to congratulate Lennon for the job he has done at Parkhead, while selling some of the club's top players, but feels he has an enormous job in sustaining the recent success.
"Celtic thoroughly deserved their league title and won it quite comfortably in the end. They've got some very good players, but they've also lost some very good players," said McCoist.
"Joe Ledley did a terrific job for them before moving to Crystal Palace. Gary Hooper scored an awful lot of goals, but he went to Norwich City in the summer. And I thought Victor Wanyama was an excellent player for them before he, too, went to England with Southampton.
"Neil will now want to hold on to his current squad and look to build for the next campaign. I believe it will be very difficult for Celtic to maintain their standards when you consider they are without real competition in the league. That's just my personal opinion. Of course, Rangers and Celtic have always provided each other with strong opposition in the past.
"Neil, though, now has the problem of maintaining the standards he has set at Celtic. He will also be looking to improve in a league you would think they would win for the foreseeable future."
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