Stoke have won just three games in front of their own supporters in 2013, and only one this season.
He told the Sentinel: "Their support has evidently been critical to our fortunes in the past and at the Britannia Stadium with the unique atmosphere they were able to create so superbly.
"That kind of support is what everyone would love to hear and then I'm sure the players will reward our fans in the long term.
"We would obviously like to get some more points and the home games are where we have done that in the past.
"I ask them to be patient because I am confident everything will fall into place and our good performances so far will be rewarded with good results.
"Away from home, I believe we have been doing pretty well in the league and on another day we could have had five more points if you look at what happened in the defeats at Fulham, Manchester United and Liverpool."
On the need to keep the fans on side, Coates added: "I want to emphasise the importance of the games coming up, especially at home and starting with Saturday's match against Southampton.
"Our lads are getting used to playing in a slightly different way and it really is important our supporters get behind them to help them at this time of transition.
"Players can be a bit edgy and nervous at home when results don't come - and that's where supporters can step in to assist them and help bring the best out of them."
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