Grabban was not at the New York Stadium for the 2-1 second-round win and although Neil refused to say if the 27-year-old had been given permission to skip the game, he confirmed that Norwich had turned down a third bid for the player.
"We have rejected three bids from Bournemouth so far and the bids that we have are nowhere near the valuation of the player," Neil was quoted as saying by the Eastern Daily Press.
"Until they get to an acceptable level, Lewis Grabban will remain a Norwich City player. That is where we stand," the manager added.
"I don't have any issue with any players. He might have an issue but I will quickly fix it.
"Regardless of what happens or what rumours are flying about or what others might say or do, that will have absolutely no bearing on what happens with Lewis Grabban or any player at this club," Neil said.
"As far as I am concerned, the bottom line is he is a Norwich player.
"Every player has got their price but it has to be our valuation, not what they think," added the 34-year-old, whose side will face West Bromwich Albion at home in the third round.
The manager also said he did not have to sell players to bring in fresh faces and predicted a frantic end to the transfer window on Sept. 1
"I don't need to get anybody out to bring someone in. We have funds available and I aim to put them to good use," he said.
"The one thing you can guarantee is we will do things in Norwich City's best interests. We are doing some work behind the scenes and we still have a week to go and it is going to be a hectic week."
But Championship (second tier) club Wolves said on Wednesday they had rejected a bid, put at 10 million pounds ($15.57 million) by British media for Afobe, a former Arsenal junior who scored 13 goals in 21 games last season.
"Wolves can confirm that a third bid from Norwich City for Benik Afobe has been immediately rejected," said a statement on the club's website.
(Reporting by Simon Jennings in Bengaluru and Steve Tongue in London; Editing by John O'Brien and Ken Ferris)
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