The Staffordshire club are second in the Premiership - the top-flight of English rugby as it stands - and have been part of the league for 15 seasons.
Lichfield director of rugby Becky Williams said it was "devastating" to miss out on the new 10-team league.
When asked if she hoped for a rethink, Williams said: "We deserve it."
Speaking to BBC Midlands Today, Williams continued: "What we, as a club, have worked so hard to do for 25 years is to get to the required standard - which we meet."
Women's Super Rugby, into which there will be a multi-million pound investment by the RFU over the first three years, is aimed at improved playing standards and increasing participation in the game.
Lichfield are the only Premiership side not to be included in the new Women's Super Rugby competition, as third-placed Aylesford will operate as Harlequins from 2017.
Centre Emily Scarratt, a World Cup winner and Team GB captain at the 2016 Rio Olympics, is among five Lichfield players involved in England's Six Nations campaign this season.
In a statement, Women's Premiership chair Mark Francis said "the competition will be weakened" by Lichfield's absence and also "welcome the RFU to reconsider the decision".
The RFU have said they are willing to work closely with the club and help "support future ambitions to compete in the new competition".
Applications for a spot in Super Rugby were based around coaching and training, sports science and medical support, training and playing environment, player pools, and financial streams.
There will be no promotion or relegation from the competition for the first two seasons, which starts in September.
While Lichfield boss Williams is disappointed the club has been overlooked, she does stress the RFU's efforts to establish a better funded and resourced top-flight competition is "absolutely fantastic".
England and Lichfield prop Justine Lucas echoed the sentiment, adding: "For the bigger picture, the RFU investing so much money into women's rugby is absolutely fantastic.
"But it is a real blow for Lichfield. We have all worked so hard this year and put so much into our club rugby, Lichfield means a lot to everyone involved."

It backed plans to issue fines initially, and only resort to criminal charges for repeat offenders.
Selling, buying and producing the drug will remain illegal and the move must still be ratified by parliament.
According to the UN Office on Drugs and Crime, almost 9% of Israelis use cannabis, though some experts believe the figure to be higher.
The move follows recommendations by a committee set up to study the issue, and moves by a number of US states and European nations to decriminalise use of the drug.
"On the one hand we are opening ourselves up to the future. On the other hand, we understand the dangers and will try to balance the two," Prime Minister Benjamin Netanyahu told his cabinet ahead of the vote.
Israeli Justice Minister Ayelet Shaked said: "Israel cannot shut its eyes to the changes being made across the world in respect to marijuana consumption and its effects."
Meanwhile, Public Security Minister Gilad Erdan added that the move was "an important step on the way to implementing a new policy that will emphasise education and treatment instead of criminal enforcement".
Under the new system, first-time personal users who are caught and confess will be fined 1,000 shekels (Â£220; $270), with this doubling on the second occasion.
Probation will apply the third time and only a fourth case would lead to criminal charges.
Israel is one of the world leaders in research into medical use of marijuana.

The officer was attacked after stopping a Peugeot van in Westmorland Avenue, Cleveleys on 2 November last year, Lancashire Constabulary said.
He suffered injuries to his torso and face.
William Ashton, 39, of Briarwood Drive, Blackpool, is due to appear before Blackpool Magistrates' Court.
He has also been charged with two counts of possession of an offensive weapon and affray.
The injured officer, 47, from the Immediate Response Team based in Fleetwood, has "recovered physically" and is expected to return to work soon, police said.
Lichfield want the Rugby Football Union to reconsider their failed bid to be part of the inaugural Women's Super Rugby competition.
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The Israeli government has taken steps to reduce the penalties for personal marijuana use.
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A man has been charged with attempted murder after a police officer was slashed with a knife during a routine vehicle check.