Midfielder Conca accepted a two-game ban from the Match Review Panel for his "brain fade" after clipping young Giant Devon Smith with an elbow to the back of the head last Saturday.
The round before, Vickery was rubbed out for four weeks for striking West Coast veteran Dean Cox in the head.
Tigers defender Troy Chaplin said the loss of the two was a blow, with the club’s finals hopes on life support.
Currently 12th, Richmond takes on the seventh-placed Bombers in a blockbuster at the MCG.
The Tigers were dismal in their round 11 meeting with the Bombers, being held goalless in the first quarter.
They limped home in an embarrassing 50-point loss but Chaplin said the Tigers were now an improved team.
"The last time we played Essendon was a disappointing game; probably one of our worst games of the year in reflection," Chaplin said on Tuesday.
"Within the first five or 10 minutes it was literally all over.
"Now we've got some momentum and we've got that little glimmer of hope and hopefully we continue that."
While the Tigers are riding high on the back of five successive wins, including last round's 27-point win over GWS, Chaplin admitted the suspension of Conca and Vickery had taken some of the gloss off.
"We're a better side with those two guys in our team and our discipline the other night, giving away a couple of 50s as well, was very disappointing,” he said.
"It's hurting us on the field so it's something we need to get better at."
Chaplin said even Conca's teammates were surprised by his uncharacteristic act.
"He's certainly not that sort of character to the people who know him,” he said.
"It was a bit of a brain fade and it caught a lot of players by surprise because Reece doesn't have that in him and he's got to wear it now and cop the punishment."
