Everton denied 'clear' penalty, rues Martinez
The loss was the fourth successive reverse Everton have suffered in the top flight following defeats to Southampton, Stoke and Newcastle United.
But Martinez feels his men were unlucky with one refereeing decision in particular, as Steven Naismith was not awarded a first-half penalty after being tripped by Gaston Ramirez.
And after surviving that let-off, Hull ultimately went on to take the lead through Ahmed Elmohamady in the 33rd minute, with former Everton man Nikica Jelavic adding to that shortly before half-time, leaving Martinez to rue what might have been.
He told reporters: "I've seen the two actions [controversial incidents] and I think with Ross Barkley it is clearly a free-kick, but it is outside the box, so I wouldn't expect a penalty for that.
"The first one is clearly a penalty for a foul on Steven Naismith. He [Naismith] is trying to bring the ball down and he doesn't see where Gaston Ramirez is - he just comes from the back and the contact unbalances him and he loses control of the ball."
After almost five months of no managerial changes in the Premier League, Neil Warnock and Alan Irvine were the first bosses to be removed from their posts over the festive period, but Martinez is adamant that the thought of him suffering a similar fate has not entered his mind.
He added: "If I could have time to think about all of those aspects [other people losing their jobs], I wouldn't be doing my job properly.
"Now is the time to find solutions internally and I need to bring the enjoyment back to my players on the pitch and that is the only concern I have. I will do that with all my energy."