City head to Villa on Saturday for Sherwood's first official match in charge following back-to-back 4-1 defeats to Manchester City and Blackburn in the Barclays Premier League and FA Cup respectively.
With manager Mark Hughes' side also struggling defensively due to a spate of injuries, and with Villa buoyed by their 2-1 FA Cup win over Leicester which Sherwood watched from the stands, many observers may feel a home victory is on the cards.
Despite that, speaking to the Evening Sentinel, Coates said: "The appointment of a new manager doesn't mean they have won the game already.
"The idea the world is suddenly transformed after bringing in a new manager doesn't ring true.
"I think it's about 50-50 statistically over whether you win or lose that first match.
"I remember going to Crystal Palace some years ago and people fearing the worst because Neil Warnock had just been appointed, but we came away with all three points."
Coates, meanwhile, has defended Hughes' decision to send defender Robert Huth on loan to Leicester despite the club's injury woes.
Huth, only recently returning from his own long-term injury problems, joined the Foxes last month for the remainder of the campaign.
Hughes, however, has suddenly lost Ryan Shawcross, Marc Wilson and Marc Muniesa, with little else available via way of cover.
Coates said: "Yes, I can understand why supporters would be asking 'why did you let him go?', but equally I can understand the management team's reasons for doing so.
"They wanted to give him games after his long-term knee injury and it was felt reserve games weren't suitable.
"We had also brought in Philipp Wollscheid to add to the centre-halves we had here.
"The timing was then very unfortunate with the injuries that followed the decision to let Robert go.
"Ryan has a wonderful appearance record, for instance, but then came that bad run of injuries which included him, Marc Wilson and now Marc Muniesa."
Source : PA
Source: PA