The Hungarian joined Barnsley on Wednesday in a loan deal until January.
The surprise move was set in motion after Buzsaky was left out of the caretaker boss’ plans against Doncaster last weekend.
That decision incensed the former QPR midfielder who had recovered from a hamstring injury to declare himself available.
He also failed to feature in Tuesday night’s defeat to Leyton Orient.
Whittingham denied it was a case of Buzsaky refusing to play.
However, he had no intention of standing in the way of a player who wanted to leave Fratton Park.
He said: ‘I am not going to say anything disrespectful about Akos because he did his best for us when he was here and he wants to play football.
‘It was just a case of I pulled him and said about him not playing, he wasn’t happy he wasn’t playing – which you understand of players.
‘He said if that was the case then he would like to go somewhere else.
‘I can understand the situation. He was at QPR last year – he played 21 games and thinks he should be starting here.
‘Well that wasn’t how the staff felt here and if he didn’t want to stay then I had no problems with him going somewhere else.
‘He is a nice lad and I hope he does well there.
‘You want people who want to play for this club, especially when you are down to the numbers we are.
‘We need everyone determined to get on to the pitch but accept it if we decide we are going to go a certain way and they are on the bench.
‘They will then do the best for us when they come off the bench.’
Buzsaky made eight appearances for the Blues, seven of them starts.
However, he failed to have the impact expected of a player who featured in the Premier League last season.
His final appearance was Michael Appleton’s last match when Pompey lost to Brentford on November 6.
After picking up a hamstring problem in training days later, the 30-year-old was ruled out of the trip to Bury.
However, Whittingham has denied rumours Buzsaky refused to play.
He added: ‘Akos didn’t decline to play in a game, he just wanted to go somewhere else.
‘That allowed us to bring Jake Jervis in as a replacement, so it benefitted us as well.’