Mitchell, who is currently out of the country, says he received a number of verbal offers for the striker during a series of telephone calls with Eagles chief executive Phil Alexander.
Ings turned in a lively display against the Championship outfit and went close to opening the scoring with a delightful chipped effort during the early stages of Cherries' 3-1 win.
Palace are among a host of clubs tracking the highly-rated 19-year-old and had a cheeky bid of £200,000 rejected by Cherries chief Mitchell last month.
Cherries have also rebuffed a £400,000 offer from Premier League Fulham with Mitchell insisting the bidding for Ings must start at £1m.
Speaking to the Daily Echo last night, Mitchell said: We had some verbal offers for Danny from Crystal Palace and they were all turned down. I had one phone call before the game, one at half-time and another one following the final whistle.
The figure went up as the game progressed and was £500,000 in the end. It had started a lot lower than that. I told them he would cost £1m-plus and said he would not be going for anything less. I am standing firm on this one and there is no room for manoeuvre.
Mitchell, meanwhile, said he had been reasonably satisfied with the transfer fee settled on for the sale of Cherries midfielder Anton Robinson to Huddersfield.
Although the figure was officially reported by both clubs as being undisclosed, the Daily Echo understands it was in the region of £250,000, with Robinson's former club Weymouth receiving £5,000.
Had the 25-year-old not been sold, Robinson, whose Cherries contract was due to expire next summer, would have been entitled to leave for nothing in 12 months.
We couldn't let the situation happen as we did with Danny Hollands, said Mitchell. Anton could have started talking to clubs in January and, realistically, you lose control after that.
Mitchell added: I am disappointed about every player sale but that is football. We have got to show what we can do this season with what we have got.
We have bought players and loaned in a couple and we have not finished yet. We are working on it constantly and will keep doing so throughout the season. We are not going to rush into anything but are working towards getting the best team possible as soon as possible. We are making enquires all the time.