The SPL side, who lost 3-0 at Rangers on Saturday, were making a return to the ground where they suffered a humiliating exit against Queens Park in the same competition last season.
After a brisk opening, Roberts blasted his spot kick against the post and the Dons survived as Thistle enjoyed the bulk of possession.
Lee Miller was denied by the woodwork in Aberdeen's first real chance after good wing play by Jamie Smith, while Roberts saw Jamie Langfield deny him from 10 yards at the other end.
The Jags were made to pay for their profligacy when Jimmy Calderwood's men broke forward and Young returned to haunt his old club to break the deadlock before the interval.
Young seized his chance after Craig Hinchcliffe parried Barry Nicholson's shot.
Aberdeen began to take more control in the second half and, although Thistle battled furiously, the Dons netted a second to effectively kill the tie.
The Glasgow outfit failed to clear the danger from a corner and the unlikely figure of Considine appeared in the six-yard box to complete an easy finish.
There were to be no more mistakes from the Dons.
The gulf in quality between the teams showed as Ian McCall's team were left, ultimately, to wonder what might have been after their first-half showing.
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Interview: Aberdeen manager Jimmy Calderwood
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