The London outfit were playing against 10 men for much of the duration, but struggled to overcome the Tigers, much to the frustration of sections of the home crowd.
Allardyce hit out at the supporters who gave his players a hostile reception, pointing out that it could be detrimental to team morale.
"I've never been in a place where I've won and got booed," BBC Sport quotes Allardyce as saying. "Fans affect players.
"We don't need them on players' backs when we are coming off three defeats. They have to stay and help them win."
He added: "I started playing at 16, got in a first team at 18 and am 59 now, but I've never been in place where I won and got booed."