McAnuff finds it hard to understand why fans head for the exit long before the final whistle.
Former Crystal Palace midfielder McAnuff, 31, said: "You would think our fans would have learned not to leave early by now.
"We never give up and we have claimed a lot of points late in games."
Reading scored three goals in the last eight minutes to beat West Brom 3-2 in their most recent home match.
However, many supporters missed the astonishing revival from two goals down.
McAnuff added: "All we ask is that fans bear with us. It is a tough season in the Premier League and I am sure everyone can appreciate that. I do not think the crowd realise how important they are to us."