The Toffees are currently sixth in the Barclays Premier League, chasing a top-four spot, and Boro are bottom of Sky Bet League One.
But while that disparity might suggest this weekend's game will be a relatively straightforward assignment for Everton, Martinez feels respective league positions count for little at this stage of a knockout competition and that "the home team is always the favourite".
The Spaniard, winner of the FA Cup last term as manager of Wigan, said: "We are all well aware of the sort of thing we are going to find at the weekend and we have to be prepared for that.
"We are going to try to be as good as we can and make sure we don't let the home side have the advantage they will otherwise have.
"I think in these rounds people forget that the divisional status counts for very little, and it is about how you adapt on the day to the conditions, surroundings and environment.
"The home team is always the favourite in these rounds, so we need to make sure we are ready to face a very difficult game."
Toffees full-back Seamus Coleman has been ruled out of Saturday's 5.30pm kick-off due to the injury he picked up in the 1-1 Premier League draw at West Brom on Monday.
Martinez said: ''The only difference from the squad on Monday is Seamus Coleman.
''He picked up a minor soft tissue injury, so he'll miss the weekend and we'll assess him from there.
''He adds to Steven Pienaar (groin) and Ross Barkley (broken toe) who are still unavailable, on top of the long-term injuries to Arouna Kone, Darron Gibson (both knee) and Gerard Deulofeu (hamstring).
''Antolin Alcaraz (muscle fatigue) is still recovering well but will be missing at the weekend.''
Regarding on-loan Barcelona forward Deulofeu, absent for the last seven games, Martinez added: ''Gerard is not too far away.
''I will be very surprised if he is not available at the end of next week."
Meanwhile, Martinez hopes the injury suffered by Monaco's Radamel Falcao does not affect the chances of Everton completing the signing of the Colombia striker's club-mate Lacina Traore.
The Toffees have been granted a work permit for 6ft 8ins Ivory Coast frontman Traore, who they are looking to capture on loan for the rest of the season.
Reports have suggested Falcao is facing a long spell out of action - that could possibly include the summer's World Cup - due to the knee problem he sustained this week, and that the setback for Monaco might mean they opt to hang on to Traore.
Martinez said: ''We hope that is not something that will affect the decision to allow Lacina to go out on loan.
''I think it would go down to what the player needs in his development and I hope that (Falcao's injury) would have no bearing on the decision.
''We are really far down the line and it would be a real disappointment not to complete it, so we will see what today brings.
''We have got the work permit and we feel quite excited about bringing Lacina to Everton.''
Martinez has also reported no news in terms of Everton and England full-back Leighton Baines' contract talks with the Toffees, only emphasising that the club are "working hard" on the deal.
He said: "It is one of those situations where we are all very excited and working very hard to achieve a positive outcome. But there is nothing to announce yet."
Martinez has indicated that similar discussions with likes of Coleman and midfielder Barkley will be focused on after the current transfer window closes.
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