There had been talk of a demonstration before the match and the chant of "Where's the money gone?" rang around the game towards the end of the match.
A few individuals also spat abuse at the chairman, but he said the perception that Millwall had lots of spare funds was mistaken.
"I can't pretend that some of the chanting on Tuesday night was pleasant," he told BBC London.
"There were a few frustrated people about. But this, in a nutshell, is the situation. The season before last we made a loss of £4.5 million. Because of our ambitions we spend more than we get through the gates.
"Last season we had a better time of it and the FA Cup run brought in about £2.4m. We sold Tim Cahill to Everton for £1.5m, not the £2m we would have got from Crystal Palace. All of that plus some is available to manager Dennis Wise and assistant Ray Wilkins to bring players in.
"They have had money to spend all summer. They have set their sights very high and we don't want to lower them. We need another three or four players. If in another fortnight we haven't got them, we might have to think again."
Paphitis wants Wise's squad bolstered by the end of the month so that new signings can play in the UEFA Cup.
He also confirmed that the club had enquired about Teddy Sheringham joining from Portsmouth in the summer and claimed they had offered another player the highest wages in the club's history but he chose to join a Premier League side.
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