Wales assistant manager Raymond Verheijen has faced a backlash following his comments suggesting that he should succeed the late Gary Speed as the national side's manager.
Roberts believes that Verheijen, who has also coached Holland and Russia, was wrong to show his eagerness for the Wales job so early in the wake of Speed's death.
"What he put on there really left a bad taste in my mouth," Roberts told BBC Wales. "Some of the things he's posted on Twitter have absolutely shocked me. It's very, very selfish. It's just over two weeks since we lost Gary and just over 48 hours since Gary was finally put to rest.
"The timing's shocking and I don't think he should be putting his CV, if you like, on Twitter. He's touting himself for the Welsh job. He's put it out there in the public for everyone to see. That's the thing that sits really awkward and uncomfortable with me.
"He's upset and angered me in the past with some of the things he's posted but nothing [compares with this]. Gary's wish? I find that quite astonishing when Gary's family are still grieving."
The Wales board met yesterday to discuss Speed's potential successors.