The midfield pairing were unavailable for selection for Chris Coleman's squad ahead the forthcoming Euro 2016 qualifying double-header that also sees Wales take on Cyprus on Monday.
Liverpool's Allen is currently sidelined with a knee injury, while Arsenal star Ramsey is carrying a hamstring complaint, and their absence will come as a blow to a Wales side who opened their campaign with an unconvincing 2-1 win in Andorra.
But Hull City centre-back Chester, who only committed himself to the Welsh national team earlier this year, insists that Coleman has the depth to cover for the influential duo.
"Joe and Aaron will be a loss because they're playing for two of the biggest teams in Europe, but we've got a squad where most of the lads are playing their football at the top level, so I think we can cope although they will be missed," he said.
"The game against Andorra was tricky, but the win was the most important thing going into these two games.
"It's a big opportunity for us after picking up three points in the first game.
"We know we've got a great chance of qualifying for a major tournament, and to do that we've got to take points from these games. It's something the country's not done for a very long time, so we can make history."
Bosnia - top seeds in Group B - suffered a shock 2-1 defeat at the hands of Cyprus in their opening encounter and will be keen to get their first points on the board as soon as possible.
There is no question both sides will look to star names Gareth Bale and Edin Dzeko for inspiration at the Cardiff City Stadium on Friday, but eight players across the two squads could be set for their international bow in the Welsh capital.
And Zeljeznicar defender Josip Kvesic is in a confident mood as he settles into life with the national team.
"First impressions are great, the other guys took me in," he said.
"The team and I expect to win all six points in the next two games against Wales and Belgium, who are a much better team than Wales to be honest."
In addition to Allen and Ramsey, Wales saw James Collins, Paul Dummett and Lee Evans pull out of the squad earlier this week, replaced by Declan John, Joe Walsh and Gwion Edwards.
Bosnia, meanwhile, will be without the injured Goran Zakaric and have question marks over the fitness of Emir Spahic - the former captain who came out of retirement in the wake of the Cyprus defeat - after the defender flew to Germany this week for further tests on a back problem.
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