The 3-0 win over 10-man Newcastle thanks to goals from James McCarthy, Romelu Lukaku and Ross Barkley was the Toffees' first in the league at Goodison Park in 2015.
It was a crucial one as it lifted them six points clear of the relegation zone and Martinez believes the basis for the performance was founded in the come-from-behind 2-1 Europa League win over Dynamo Kiev on Thursday.
"It was a big game for us and sometimes that can bring extra pressure in that you play the occasion rather than the game," he said.
"The perfect preparation was Thursday. Probably Thursday was a real turning point in that moment when we managed to take control of the situation.
The first 20 minutes (against Kiev) was as bad as it can be in terms of suffering because you feel the anxiety and responsibility as a player then all of a sudden we found the way we should perform.
"The mindset today wasn't of a team who had fear of losing at home, some of the play was outstanding but when we had to defend and work hard for each other we did that with total composure.
"From scoring the first goal we managed the game really well and I thought we defended really composed. Tim Howard had a big save in the second half but apart from that I thought we protected him very well.
Everton were already 2-0 up when Magpies captain Fabricio Coloccini was sent off for a lunge at winger Aaron Lennon and Martinez had no doubts about the straight red card.
"I haven't seen the replay but I thought it was reckless and high," he added.
"If you look at the reaction of the Newcastle players I don't think anyone was surprised when they saw the red card.
"I don't think it was a turning point or the reason why we won because we were very much in control but it always helps."