The Rossoneri currently trail Serie A leaders Juventus by a point with just two rounds remaining and it has been reported that their 44-year-old coach will be sacked if the Scudetto is not retained.
However, regardless of the outcome of the title race, Shevchenko believes that Allegri has done a good job again this season, particularly in light of his old side's well-documented injury problems.
"With him, Milan have started to play differently and, in my opinion, better," the former Rossoneri striker told the Corriere dello Sport.
"He's a very pragmatic coach, has a great determination and never gives up. In these two years he has been able to handle the injury situation very well."
Shevchenko is now praying that Milan triumph in Sunday night's meeting against city rivals Inter at San Siro in order to keep up the pressure on Juve, who face Cagliari in Trieste at the same time.
"I hope, of course, that AC Milan win as it will keep them in the fight for the title," he admitted. "Juve are the masters of their own destiny but Milan is still in the running.
"However, Inter will absolutely want the victory in order to try to finish in third place. It 's true that this has not been a great year for the Nerazzurri but the derby always disregards the odds."
The Derby della Madonnina kicks off at 20.45 at the Giuseppe Meazza.