The broadcaster took to Twitter to launch an attack on Mr Wallace with a tweet that seemed to resonate with many other users on the social media platform. However, Mr Neil seemed to have got the moderator’s name wrong as he referred to him as Mike Wallace.
In the tweet, he wrote: “Mike Wallace speaks too much and his questions are too long.”
He later corrected the tweet adding: “Make that Chris. I knew his father, Mike.”
One Twitter user wrote: “Clearly a Trump Bias, his ability to moderate in abysmal, he constantly allows Trump to interrupt.
“I stayed up for this? Time to make a cup of tea.”
Another added: “Not too long, but very incoherent mumbling point scoring replies and going off of subject matter in hand.”
One said: “Totally agree! But then not many have your interview skills, you are are a master when it comes to interviews.”
Commenting on Mr Wallace’s interviewing technique, another used added: “Yes, he (Chris) is putting too much of himself into the debate.
“We didn’t tune in to listen to him.”
Mr Neil wrote: “Biden on the ropes re lack of support from law and order agencies.
“Wallace steps in and saves him!”
He added: “This is not a debate. It’s a squabble.”
Tonight’s debate is the first of its kind between the two candidates, current President of the United States Donald Trump and former vice president Mr Biden.
The showdown saw Mr Biden brand Mr Trump a clown and “the worst president that America has ever had,” and President Trump repeatedly talking over him.
When asked why Americans should chose him as the next leader over Mr Trump, Mr Biden said the President had made the US “sicker, poorer, more divided and more violent.”
He said: “When I was vice president, we inherited a recession. I was asked to fix it. I did.
“We left him a booming economy and he caused the recession.
“With regard to being weaker – the fact is that I have gone head to head with (Russian President Vladimir Putin) and made it clear to him we’re not going to take any of his stuff.”