Mitchell admits he has been disappointed with attendance figures this season, particularly in view of Cherries' lofty standing in League One.
And although crowds at Dean Court are up by more than 1,000 on last season, Mitchell feels Lee Bradbury's men deserve more support from the Dorset public.
Cherries are expected to set a new attendance record for the redeveloped Dean Court when neighbours Southampton visit in nine days' time. But Mitchell insists Saturday's clash against promotion rivals Oldham Athletic is just as important to Cherries and is hoping for a sizeable crowd.
He told the Daily Echo: I know Oldham have had a bad run of results recently but they are still a good team to be where they are. They are certainly not going to be a pushover and we are going to need all the support we can get.
The players have done superbly to get this far and that 12th man could make all the difference. We would very much like to crack the 8,000-barrier against Oldham.
Mitchell, who has seen average home attendances rise from 5,719 last season to 6,803 in the current campaign, added: We are disappointed we are not getting a few more. If you compare this season with last and when we first came in, they are creeping up but it is a slow process.
Meanwhile, Mitchell confirmed talks with a new stadium sponsor were very advanced and said he hoped to reveal more details in the next few weeks. Cherries' existing deal with Classic Eyes is due to finish at the end of this season.