Network Rail have admitted health and safety breaches after two girls, Olivia Bazlinton, 14, and Charlotte Thompson, 13, were hit by a train at Elsenham station footpath crossing in Essex in 2005.
Olivia's father Chris Bazlinton said the move "proves that we have been lied to over the years".
Charlotte's father Reg Thompson said "in the aftermath of the accident, Network Rail claimed the girls had acted recklessly and that somehow their youthful exuberance led directly to their deaths, as if exuberance itself is a crime.
"I never believed that they were the architects of their own terrible end. It has taken six years to reveal the truth of what happened."
Olivia's father Chris Bazlinton added: "It's not over yet. I have no doubt Network Rail will change its procedures to ensure that action is taken when problems arise, and to avoid a cover-up happening again.
"But I think this should be transparent and open. I want to know what they are going to do to change the way they report on accidents and how they account for them.
"And above all, we shall be watching closely to make sure that the changes Network Rail has promised to improve level crossing safety are carried out.
"Visions and plans are all very well, but it is putting them in place that matters."
The parents of two girls killed in a level crossing accident pledged to continue their fight for improved safety after the train company admitted health and safety breaches.
Network Rail (NR) indicated guilty pleas to three charges under the Health and Safety Act at Basildon Magistrates' Court and was committed for sentencing.
Charlotte's father said: "The horror of that day is always with us and the huge hole in our lives left by Charlie will never be filled.
The fathers have led a long-running campaign for NR to admit fault. Mr Bazlinton said: "There can be no doubt that this has been a cover-up."
Network Rail said it would plead guilty to failing to carry out a sufficient risk assessment, failing to properly control protective measures at the level crossing and failing to prevent the girls from being exposed to the risks which led to their deaths.
Prosecutor Sarah LeFerve said the magistrates' court's power to impose a maximum fine of £30,000 for the offences was insufficient, given their gravity.
Network Rail will be sentenced at Chelmsford Crown Court on March 15.
Defence counsel Prashant Popat said: "Network Rail has already privately expressed regret and remorse for this tragedy.
"Today it accepts publicly that these faults caused the deaths of these two girls."
Olivia and Charlotte were killed on December 3 2005 as they crossed a footpath leading to Elsenham station platform. The crossing was fitted with warning lights and yodel alarms.
A London to Cambridge train passed over the crossing with the red lights and yodel sounding - a warning for foot passengers not to cross.
After the train passed, the lights remained on and the alarms continued to sound as another train, travelling from Birmingham to Stansted Airport in Essex, was going to pass through the station.
The girls opened the unlocked wicket gates and walked on to the crossing. They were both struck by the Stansted train and killed.
In a statement released after the hearing, David Higgins, chief executive of Network Rail, said: "Last year I apologised in person to the families of Olivia and Charlotte. Today, Network Rail repeats that apology.
"In this tragic case, Network Rail accepts that it was responsible for failings, and therefore we have pleaded guilty.
"Nothing we can say or do will lessen the pain felt by Olivia and Charlotte's families but I have promised them that we are committed to making our railway as safe as possible.
"In recent years we have reassessed all of our 6,500 level crossings and closed over 500. I accept that there is still a long way to go but we are making progress."
A spokesman for the Office of Rail Regulation (ORR), which brought the prosecution, said: "Our thoughts are with the families of Olivia and Charlotte. ORR will do everything it can to ensure that the prosecution proceeds as quickly as possible."
Today's court hearing comes after 15-year-old Katie Littlewood was hit by a train at Johnson's Footpath Crossing in Bishop's Stortford, Hertfordshire, on Saturday.
Her death, which is being treated as a "tragic accident" by both Network Rail and British Transport Police (BTP), occurred just a few miles down the same stretch of track where Olivia and Charlotte were killed six years ago.