Spurs travel to Villa Park on Tuesday for the third-round clash, barely 48 hours after their 1-0 Premier League win at Cardiff.
The game will take place on Tuesday due to Birmingham and West Brom being at home to Swansea and Arsenal respectively on Wednesday, and concerns over the potential impact on crowd safety due to policing demands.
Villas-Boas understands the reasoning, but it has done little to improve his mood.
"This is an impossible game for us to play, but hopefully our team spirit and motivation can get us through," he said.
"It (the Capital One Cup) is not our absolute number one priority but I don't think we have been given a fair chance to play in this competition this year.
"It could be possible for the players who played against Cardiff to play this game, but I am not sure I want to risk the players who played getting a hamstring injury which could take them six weeks to recover from when the Premier League is more important.
"This team has not experienced having to play again after just two days and we have not been given the same chance as the other teams. So we will have to rotate our squad as the players who played in Cardiff will not be involved.
"We are struggling a little bit with injuries but we have great strength in depth, although it is not going to be easy."
The Portuguese feels the extra 24 hours Villa have had to recover and prepare could prove decisive.
"It is difficult, the ideal situation for us would have been to play Wednesday," he said. "I understand the situation for the police with a number of matches being played in Birmingham, but we do not have the same chance as other teams.
"Villa will not have to do the same (in terms of squad rotation) as they played on Saturday, so they have had an extra day of recovery."
But Villas-Boas is confident he will have full-back Rose available for the weekend meeting with Chelsea.
"Danny's injury is not on his ankle, it is on his big toe," he said.
"We have good news in that there is no fracture but there is another extension of the toe which has left him with some pain.
"We will reassess him and if he is okay and there is definitely no fracture he will probably be back for Chelsea."