Everton have lost their last three Premier League games, ending what has largely been a positive 2014 on something of a low note, and lie 12th in the table after Sunday's 3-2 defeat to Newcastle United.
The positives of a fifth-place finish in Martinez's debut campaign have faded somewhat, with the Spaniard acknowledging that this is the toughest period of his reign at Goodison Park.
Missing goalkeeper Tim Howard (calf) and with doubts over Phil Jagielka (ankle) and Leon Osman (foot), Martinez wants to see his side tighten up defensively to maintain their strong recent record against Hull.
Everton are unbeaten in four meetings with the east Yorkshire outfit and won 2-0 at the KC last season, while Martinez feels Hull are also struggling to match their achievements earlier in 2014.
"We have become a bit more open and exposed in terms of conceding goals. That's from errors and bad luck but we need to get rid of that negative momentum," he said on Tuesday.
"Hull are a little bit suffering with confidence and started the season with huge expectations after reaching the FA Cup final.
"When you don't get results you get doubts and opinions from outside but now we are stronger than ever in terms of what we want to do and how we want to do it.
"We need to focus in on the next game and Hull is the only game that matters.
"They had new signings coming in [the close-season] and have had an up and down season but they are going to be well organised and energetic.
"It's a difficult place to visit but it's a vital game for both teams, for more than just the result."
Hull were unable to build on their win over Sunderland on Boxing Day - going down 1-0 to fellow strugglers Leicester City two days later.
With just seven points from their last 12 games, Steve Bruce's side are out of the relegation zone on goal difference alone.
Speculation linking manager Steve Bruce to the Newcastle job, with Alan Pardew seemingly set to leave for Crystal Palace, will have done little to lift the mood around the KC.
However, the former Sunderland boss - who has doubts over Gaston Ramirez (groin) and Andrew Robertson (hamstring) - believes Hull's fans can prove the key on Thursday.
"Everton on New Year’s Day is undoubtedly a huge fixture for us and it is important that our fans continue to get behind the team," he told the club's official website.
"Victory over Everton could be the springboard we need going into 2015 and I ask our fans to get right behind the lads and be our 12th man."
