It doesn't but it was written much earlier!
Thing is, in the course of the war it's made clear and in places in dialogue that Starfleet lost hundreds of ships during the war. In one episode alone (I think at the start of Season 6) Bashir states over a hundred ships lost in one engagement. So whatever it might be I really do realistically feel the fleet was somewhere in the four digits before the War kicked off. Where exactly, I dunno, but it had to have been a LOT.
I would wager the TOS fleet would have been significantly smaller though.
'If the Apocalypse starts, beep me!' - Buffy Summers
'The sky's the limit.....' Jean-Luc Picard, 'All Good Things'
courtesy of Saquist