Leighton Baines secured the points with a well-struck second-half winner but the full-time whistle prompted many banners to be unfurled calling for Martinez to be sacked.
During the game an aeroplane circled above Goodison Park trailing the message: "Time to Go Roberto".
Everton's slide was at least halted by three overdue points, but a week after an FA Cup semi-final defeat and with a hammering by Liverpool fresh in the memory, Martinez's future still looks to be in serious jeopardy.
"The win was very important -- it has been an emotional time. We had to win. We had to dig deep, we showed we were a team and that we have character," the Spaniard said.
Asked about the protests, he added: "Those aspects are not for me. My concentration is preparing the players and preparing for the game."
A clash between teams with little to play for apart from pride began in lively fashion with two goals in the opening 10 minutes.
First Tom Cleverley fired Everton ahead with a neat turn and shot but Bournemouth responded almost immediately with Marc Pugh rolling the ball home from close range.
Fears of a ninth home defeat in all competitions this season for Everton subsided, however, when Baines scored the winner, slamming home Aaron Lennon's cross.
(Reporting by Martyn Herman, editing by Pritha Sarkar)
Share
