Pearce completed a move to Leeds, worth around £500,000 at the end of last week.
It is a bargain fee for The News/Sports Mail player of the season which has been questioned by some Blues followers.
As part of the agreement, Bournemouth are also entitled to 10 per cent of the deal, a stipulation inserted when the 24-year-old Pearce was signed from the Cherries last summer.
For Birch, though, selling Pompey’s skipper was a necessity as he seeks to keep Pompey alive.
At present, there has still to be a bid for the club from any prospective owner.
And the Blues’ administrator admits as long as that is the case, there will continue to be departures among Michael Appleton’s playing ranks.
He said: ‘I am aware there is going to be criticism over the fee (for Pearce). You are always going to get that.
‘But we do the best deals we can. Let’s not forget, we have not got a very strong hand.
‘We are on a deadline and other clubs know we need to sell our assets.
‘In fact, anybody paying anything at all is an achievement in the absence of a concrete bid from a party (prospective owner) and the possibility of liquidation.
‘We do not want to sell any of these players, but it is a necessity. We are losing money hand over fist. There are ongoing costs so anything raised goes straight into the company.
‘We will need to raise whatever we can get and if we need more time to get a new owner then the sale of players gives us that.
‘This is a crisis situation and always has been. At one stage we were not sure if we were going to make it until the end of the season.
‘It is about taking things day-by-day.’
The deal with Leeds for Pearce sees Pompey receive the fee in full, rather than instalments.
It also includes a 20-per-cent sell-on clause.
Unquestionably, Leeds boss Neil Warnock has himself something of a cut-price signing.
That has upset plenty of the Fratton faithful, with many of Pearce’s team-mates expected to follow.
Yet Birch acknowledges he is in no position to play hardball, with cash injections urgently required.
He added: ‘With Jason, there is also a sell-on from Leeds worth 20 per cent.
‘It is about keeping this club going and other players will be following.
‘We are still talking, still trying to push other deals over the line. It’s all going to be very tight.
‘Of course, there is no guarantee it will all work out. A new owner is still required very soon.’