Both clubs sought an alternative date, with the possibility of moving the fixture forward by 24 hours to April 1.
This change would have benefited Everton, as they face Arsenal at Goodison Park less than 72 hours later on Saturday lunchtime.
Liverpool, too, would have gained an advantage, given their away match against Fulham on Sunday, April 6.
Arsenal appear to be the biggest beneficiaries of the current scheduling. Mikel Arteta's side host Fulham on Tuesday, April 1, meaning they will have more rest than both Merseyside clubs before their respective matches.
The Premier League confirmed its April TV fixture changes on February 28.
It remains unclear when Liverpool and Everton formally submitted their request, but the Premier League's refusal means both clubs must now manage a congested fixture period.