Everton won 3-1 last time they met Villa at home for an FA cup tie
Church-founded football clubs should remember their Christian roots, the Archbishop of York, John Sentamu said.
Church leaders have called on the government to use Sunday trading laws to prevent Premier League matches being held on Easter Sunday in the future.
Aston Villa drew 3-3 against Everton at Villa Park and Manchester City v Fulham match at the City of Manchester Stadium kicked off at 1610 BST.
The Premier League said it had delayed the kick-off to minimise disruption.
Concerns were raised last week by Birmingham church leaders, who wrote to the Premier League over concerns Easter Sunday services would be disrupted because of road closures and safety fears.
Excluding Christmas there are 363 other days of the year when we can play football.
Reverend Andy Jolley, vicar of the parish of Aston and Nechells, Birmingham
However, bosses at Aston Villa said: "We believe we have done what we can to ensure that those attending places of worship close to the ground are not inconvenienced in any way." It said it had had also paid for extra policing on the day.
But Dr Sentamu, said the matches should not be happening in the first place and asked the clubs "did you forget your history?"
Aston Villa Church Bible Class formed a football team in 1874 and the members of St Domingo's Bible Class began playing football at Stanley Park in Liverpool in 1878, becoming Everton a year later.
Dr Sentamu, the former bishop of Birmingham, said there was a "time and a place" for football which was not on Easter Sunday.
He added:"Do not think...22 people chasing a ball around is all life is about."
'Power of television'
He spoke of the clubs' church foundations and attacked the commercial nature of the sport.
He said: "What was local enjoyment and exercise has lost all meaning, they have become businesses and that is not on."
Reverend Andy Jolley, of Aston and Nechells, in Birmingham, who wrote to the Premier League last week, said he acted despite being a Villa season ticket-holder.
Mr Jolley told the BBC: "Don't get me wrong, I am a football supporter... but I would like to see this day particularly kept free from football.
We are not forcing religion down people's throats, says Archbishop
"Excluding Christmas there are 363 other days of the year when we can play football." He said residents and Villa fans had told him the games were inappropriate "taking place on Easter Sunday."
He said: "Obviously Aston Villa's roots are in the Methodist Church and I think their constitution originally forbade them to play on Good Friday particularly, because it was a holy day.
"It seems very clear the reasons it is taking place is because the television people want it to be taking place on this day."
Mr Jolley said the focus should simply be on Easter Day being "really special".
Dr Sentamu added: "The amazing thing about England is that we are not trying to force religion down people's throats, but there is a culture, a tradition, a way of behaving."