The Bhoys recorded a narrow 1-0 victory over Partick Thistle on Saturday, with Leigh Griffiths' injury-time winner handing Celtic an unconvincing win.
The three points did little to ease the ever-mounting pressure on manager Deila, with many Celtic fans keen to see the Norwegian lose his job after overseeing the club's exits from the Champions League and Europa League this season.
Celtic are top of the Scottish Championship, but with recent slip-ups - such as the home defeat to Motherwell last month - there are major concerns that Aberdeen could seriously rival the Bhoys this season.
Now, former Celtic striker and current pundit Andy Walker has told Sky Sports that he has spoken to Celtic supporters, and they are all unhappy with Deila's reign, stating that they want to see a more entertaining brand of football on offer at Celtic Park.
"I've spoken to about half a dozen Celtic supporters; every one of them unhappy with the product they see on the park," said Walker. "I don't think you can kid thousands of Celtic supporters, and what they want to see is a better product on the park, more entertainment."
Walker continued, stating that Celtic's recent recruitment hasn't been good enough, and highlighted two particular transfers to show how much money is being wasted.
Winger Derk Boerrigter and striker Stefan Scepovic, signed from Ajax and Sporting Gijon respectively, have arrived at Celtic in recent years, and made absolutely no impact - and Walker believes Celtic need to bring in better players than those two.
"They'd certainly like to see some better recruitment. I think when you look at the amount of money Celtic do spend, getting the likes of Scepovic and Boerrigter in, that's the best part of £5m, and when Celtic spend that kind of money you expect to see a bit of evidence on the park that they are improving, but those two players for a lot of money have done absolutely nothing," he added.