Reverend Irene Wilson was leaving Holy Trinity Church in Hull at 13:30 BST on 7 August when her vehicle was targeted.
Jay Desborough, 17, and Leon Wrigglesworth, 13, both from the city, were each given a 24-month detention and training order in a young offenders institute at the city's youth court.
Rev Wilson said it had "affected myself and the work that I do".
The pair had only known each other for a week before carrying out the carjacking, the court heard.
As well as having her car stolen, Rev Wilson's handbag containing Â£250 in cash and a laptop computer were also taken.
In court, the vicar described how her daughter, who she was speaking to on the phone at the time of the attack, was "still traumatised from hearing my screams".
Robin Smith, the solicitor defending Desborough, told the court the teenager had asked a family member to send an apology letter and a bouquet of flowers to the vicar as an apology.
But Rev Wilson, who was in court, confirmed it had not happened.
The vicar said she had "at all times tried to understand the culprits" and asked people to "pray for the two young men, that they will make a positive decision".
Sally Robinson, the Crown Prosecution Service's reviewing lawyer, said: "This was a shocking attack carried out in broad daylight on a respected community figure.
"Our thoughts remain with Rev Wilson as she continues to recover from the effects of this crime."
Chairman of the bench Vincent Bergin lifted a ban on naming the teenagers.
Desborough, who was aged 16 at the time of the attack, admitted to one charge of robbery at a previous hearing.
Wrigglesworth denied robbery but was found guilty following a trial.
He was also convicted of 15 other offences.
Two boys who dragged a vicar out of her car in a "shocking attack" as she left a church service have been sentenced.