Emily's family said the judge had shown compassion to the "very fortunate" couple but they felt the sentence was "just".
Their son was also sentenced to nine months, to run concurrently, for perverting the course of justice.
Sentencing the couple, Mrs Justice Dobbs said: "I appreciate it must be very difficult for a parent when faced with the situation you found yourself in but you well knew what you did was wrong and against the law.
"You gave no thought to the consequences for your youngest son and now he is going to be without his parents for an important part of his development."
She said the act of destroying a confession letter was a "very serious offence" and added: "It strikes at the integrity of the criminal justice system."
She said: "It was one act of destruction but in a sense it continued because you didn't have the guts to go to the police and tell them what you had done."
The judge said that she understood that Mrs Turner was still coming to terms with the fact her son was a convicted murderer.
She added: "I take into account you are people of previous good character and from that you have not been sentenced to a term of imprisonment before.
"People speak highly of you both and it's a tragedy that you, who are both respectable people, have lost that by acting out of misplaced loyalty.
"It must be hard for you to come to terms with what the jury found your son did."
Speaking of Elliot's younger brother, Mrs Justice Dobbs added: "He has had to live with the knowledge that his brother was convicted of murder and, if that was not enough, his parents have been convicted of a serious offence and that must be a heavy burden to bear and he has lost his friends because of this."
Speaking of Mr Turner, she added: "You have expressed remorse for Emily's death but for your own actions you have shown precious little."
The court heard that Mr Turner destroyed the confession letter written by his son with the knowledge and agreement of his wife.
Mrs Turner also removed a jacket from the crime scene as she feared it would have implicated Elliot.
Their actions were uncovered when police bugged their house and recorded conversations where they discussed whether they had done the right thing.
The court heard that Mr Turner had been made redundant and was suffering from depression and illness.
Robert Grey, defending Mr Turner, said he had acted when his "mind was in turmoil" at discovering what his son had done.
He said: "He has to live with the fact his son is a convicted murderer. He has two children, the oldest is a convicted murderer and he has to live with that for the rest of his life and his son is in prison for a very, very long time.
"That knowledge can itself amount to a form of punishment and the court knows his life has been affected by what has happened in the past 15 months or so.
"It's not just his mental health, it's his physical health.
"The defendant is deeply depressed."
Fern Russell, representing Mrs Turner, said: "She is a mother who couldn't accept that her son had committed the worst imaginable crime and it was in that turmoil that she carried out that act.
"In her mind she wasn't concealing a murder but at worst was buying time for her son to explain himself."
Mrs Justice Dobbs told the defendants that the offence deserved a term of three years but she had reduced it because they had both "suffered" from their son's actions and also out of concern for their other son.
Speaking outside court, Emily's grandfather, Ron Longley, said: "Today brings a sort of conclusion to a dreadful year.
"Mr and Mrs Turner are very fortunate in how much compassion the judge showed in the mitigating factors and in reducing their sentence.
"We are satisfied with the sentence, we feel it was balanced and just.
"A year ago, Mr and Mrs Turner's son murdered my granddaughter Emily, our lovely, shining Emily.
"This presented Mr and Mrs Turner with a dreadful dilemma. They made the wrong decision.
"As a result, we and many other people have spent a long year and more waiting for this and now they are suffering.
"Because of their actions, the police were forced into a prolonged, protracted and expensive inquiry. Thank goodness they were so very thorough and professional - we will be forever grateful for them for that."
When asked if he believed his family had received justice, he said: "In law certainly. Morally, in terms of life, we can't feel that anything has been made fair."