League One side United, who overcame Aston Villa 2-1 in the third round, looked set for a second straight Premier League giant-killing on Sunday when striker Chris Porter gave them the lead after 31 minutes.
However, United saw captain Michael Doyle sent off for an off-the-ball altercation with Chris David early in the second half, before Fulham secured a replay through Hugo Rodallega's 75th-minute strike.
Clough's men had been denied a penalty prior to the equaliser, despite Aaron Hughes' trip on Ryan Flynn - a decision that angered both Clough and his players.
"I thought it was an incredible cup tie," Clough said.
"It was a remarkable effort by the players - especially with 10 men.
"I thought there was more contact when Ryan Flynn went down for the penalty than there was for the sending off.
"The players have come off feeling a sense of injustice."
‘The pure simplicity of the way Slot has managed the squad is probably the biggest thing I could say about him. It’s not broken, so let’s get on with it’: Liverpool legend full of admiration for Jurgen Klopp's successor at Anfield
‘I trained at Spurs and thought they’d give me a chance. But I received a letter thanking me but saying they didn’t think I was good enough – I was gutted’: How Tottenham missed out on signing Wales legend John Toshack
