Romelu Lukaku scored the winner from the penalty spot in the 82nd minute to become the club's record goal scorer in European competitions, as Everton seized the first-leg initiative in the last 16 tie.
Everton's Europa League form is in stark contrast to their Premier League fortunes, with Martinez's men languishing 14th in the table.
But the Spaniard believes his side can now turn the corner.
"For me it is a turning point in the season," he said.
"In terms of understanding what's been going wrong this campaign, when we haven't been able to develop a moment in the league and show what a good team we are when we have the right mindset."
The former Wigan Athletic boss has now challenged his team to finish their domestic campaign strongly.
"Our focus now is what we've got in front of us," Martinez said.
"The 10 games we've got in front of us is the opportunity to show that we can finish the season really strong, that we can get a really positive feeling about what we can achieve, and that starts with Newcastle."
Martinez also confirmed that Leighton Baines (groin) and John Stones (illness) face late fitness tests ahead of the game, while Aiden McGeady and Steven Pienaar are close to re-joining the squad after long lay-offs.
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