After the fifth-round game at Brisbane Road, second-placed Arsenal host Stoke city next Wednesday in the Premier League before facing Birmingham City in the League Cup final the following Sunday.
Three days after a league match at home to Sunderland the Londoners head to Barcelona on March 8 for the second leg of their Champions League last-16 tie, which they lead 2-1.
"We are involved in every competition and that's why our destiny will be made by how much we can get focused every time," Wenger told reporters on Friday.
"By how much we can mobilise our resources in every game, how much the whole squad is concerned and so for us the intelligent attitude will be every time just worry about the next game."
Arsenal have not won a trophy for six years and the Frenchman is not about to limit his options at this stage by prioritising too much.
"We want to go for every competition," he said. "I believe we can go in every one to the end but it can also stop very quickly. It's down to how much we believe and how much commitment we show.
"I'm convinced we have the hunger and we have some talent and we are all committed to go as far as we can."
With League One Orient having already upset Championship Norwich City and Swansea City in earlier rounds and having lost only one game in their last 20 in all competitions, Wenger is bracing himself for a stiff examination in east London.
"We had tough games against Leeds, Ipswich and Huddersfield so we have been warned about how difficult it is," he said.
