After Coventry avoided relegation from the Championship by the skin of their teeth last season, Coleman is targeting a top-half finish for this campaign before taking the club on to the next level and a push for the play-offs next term.
"I think the fans are buying into our expectations now," said Coleman. "I often put myself in our supporters' shoes and over the last seven or eight years they have probably had so many empty promises and have had the feeling that this is going to be their year and it never happens.
"But I think they have realised now, let's hold on a minute, this is going to take time and maybe we need to be a little bit patient.
"We are making progress and we will strengthen the squad again in the summer to help us achieve what we want to achieve next season, which is to be challenging in and around the top eight or six."