The Latics dropped the third match in a row to make it four losses in their past five which has them sitting 18th on the Premier League table.
Arouna Kona gave Wigan some hope with an 82nd minute goal after Leon Osman and Phil Jagielka gave the Toffees a two-goal lead but it wasn't to be, leaving the Spaniard with a massive headache after seven losses from nine outings on the road this campaign.
"I'm frustrated and angry. It is a moment of the season where results are starting to be very important," said Martinez.
"We knew we were coming to a difficult place but the way we played the first half, I thought we stopped them from having any momentum.
"We were starting to get into a good position to get a positive result and actions in both boxes cost us.
"We need to make sure we don't rely on third parties - we don't rely on decisions to get positive results.
"We will learn from it. It is not good enough just to play well in the Premier League, whichever ground you are playing at.
"If we need to play extra well to get a positive result, that is what we have got to do."