The second round defeat at Notts County saw the club miss out on £27,000 in prize money and a potentially lucrative tie against Premier League Sunderland.
That setback came against the backdrop of the testing financial climate and during a period when Cherries have just one home fixture sandwiched between three away games.
But Mitchell says the Dean Court outfit are finding a way to get by.
When asked if missing out on a third round tie at the Stadium of Light was a big blow to the coffers, Mitchell told the Echo: We'd have preferred to win it and get the money, but it was not something we had in our cash-flow.
I think everybody likes to have a little windfall now and again but it wasn't to be. We'll manage.
We planned for half the gate money at Notts County and that's what we got.
He continued: The finances are probably the same as I have said before.
Like most of the country, it is very difficult. But we're finding a way to pay our way, and we're going to continue to do that.
Mitchell, who confirmed Cherries were paying their stadium rent while also eating into backdated money owed to the landlords, provided an insight into the financial battle facing the League One outfit.
He said: It's very tough. We've all had to dig deep but we're not alone.
You can see that by the students demonstrating about having to pay more money, retailers worrying about where their customers are coming from and job losses.
We're all not where we were four or five years ago but we're getting by and that's the main thing.
The restaurant upstairs at Dean Court for Sunday lunches has taken off and we're averaging between 80 and 100 people each weekend, which is good.
The bistro has opened and, at lunchtimes, we're quite busy. It's good and it's adding to the coffers.
Meanwhile, the Cherries chairman has dismissed speculation linking playmaker Marc Pugh with a £200,000 move to Southampton.
Mitchell said: I think he's worth a lot of money he's a very good player and he's |certainly worth more than £200,000.
We don't want to lose him and we're not going to lose him, as far as I'm concerned.