Patrick van Aanholt’s free-kick and two close-range strikes from Lamine Kone sealed a comfortable win for Sunderland at the Stadium of Light which secured their survival and relegated Newcastle and Norwich.
Spaniard Martinez, who took over from David Moyes in June 2013 and signed a new five-year contract in 2014, added: “The effort we put in deserved a lot more.
“It was not an easy game and Sunderland had a lot of momentum with their focus on the league.
“We have one more game to get the winning feeling and perform in a manner in which we can get the three points and end the season better.”
Everton finished fifth in the table with a record Premier League points tally in their first season under Martinez in 2013-14, and 11th the following year.
They end their campaign at home to Norwich on Sunday.