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Oxley was booked for time wasting - his second yellow card of the competition - and will be suspended for the semi-final against Dundee United.
The 25-year-old Englishman was subsequently taken off to be replaced by Finnish debutant Otso Virtanen.
"He lost his contact lens," manager Stubbs explained.
"He has asked the ref [to try to find it] but he [the referee] will probably hide behind the fact that Ox didn't say that.
"But it was obvious to everyone in the stands that he had a problem with his eye, and there was a problem with communication."
Victory at the Caledonian Stadium came three days after Hibs lost the League Cup final to Ross County and follows a run of three defeats in the Championship.
And Stubbs insists criticism can only drive his team on, with Anthony Stokes' double securing a swift return to Hampden for the meeting with United.
"I couldn't care less what people say about our team. The most important thing is what we say in the dressing room," Stubbs told BBC Scotland.
"When you do well, there are always people ready to criticise, but that is part of the game.
"I will never doubt my players. I believed in them even on the back of this horrendous run we have had, and the lads showed great character tonight.
"We have got to a final, and now another semi-final, and we still have a chance of promotion. Sometimes people write you off after one result, but they can keep going as far as I'm concerned. All it does is make us stronger."
"The strikers deserve a special mention. They looked back in form, considering they were out of form. Stokesy scored two and Jason could have scored again. We have come to a Premiership team and had a lot of chances. The lads at the back have had to stand up to a real onslaught of balls into the box too."
Iain Vigurs netted a consolation for the hosts and Caley Thistle manager John Hughes said: "We beat ourselves with the goals we conceded in the first half. They were very poor goals.
"We huffed and puffed in the second half but it was a little bit too late.
"It wasn't a great game but to be fair to Hibs, they probably edged it.
"I picked a team that would really go toe-to-toe with them, but it didn't really materialise."
Alan Stubbs described losing Mark Oxley for the next round as "the only real downer" of Hibernian's 2-1 Scottish Cup replay win over Inverness.