There were protests against the Toffees boss during the 2-1 win over Bournemouth on Saturday, with a plane trailing the message 'Time to go Roberto' followed by around 100 fans armed with 'Martinez Out' banners remaining inside Goodison Park for over an hour after the final whistle.
It remains to be seen whether the Spaniard can ride out the storm as only a fifth home league win in the last 12 months has done little to change the minds of a growing number of disgruntled supporters.
Martinez has come under fire for his style of play - something he was lauded for in his first season which accrued a club-record Premier League points tally - contributing to them dropping points from winning positions.
The players have escaped almost scot-free as the manager has borne the brunt of abuse, but goalkeeper Howard said that does not reflect reality.
"Everyone talks about the manager but he hasn't kicked one ball this season," said the United States international.
"It is down to us as players
We are the ones who have to be resilient and dig in
If that hasn't been good enough, fair dos.
"We have to take that on the chin
The table doesn't lie.
"Everyone is entitled to their opinion so I don't want to comment on plans and banners but we have to kick the ball, try to save it, try to score.
"Whatever happens on the outside is where the game has gone, whether that is right or wrong people have a right to voice their opinion and that is what people do.
"Every manager needs to be given time
People can't have it both ways.
"Often you get everyone outside of a club talking about players who are not loyal but it works the other way too.
"People need to be given time when they come to a club - players, managers, the board, it is no different."
There have been murmurings that Martinez has lost key members of the dressing room and that players are no longer playing for their manager.
Howard takes that as an insult to their professionalism however.
"I love this club and I feel it is the greatest club I have ever played for but we have no divine right to win games and we have to roll up our sleeves and dig in, and we haven't done that enough," he added.
"When you play professional sports you are open to criticism good and bad and I always say you are never as good or bad as people say you are.
"One thing I can assure everyone is we are going to work and we try our tails off to win football matches, no-one chucks it in.
"I think as senior players you try to protect the younger ones because they've not seen it before but I'm an old dog and I've seen it all before.
"No criticism fazes me; not from the media, outside sources or social media
It is just words.
"We have to go to work every day and try to get it right.
"It isn't fantastic and we will try to reel off three more wins and try to get ourselves up the table."
Midfielder Tom Cleverley gave Everton an ideal start with a crisp strike after just seven minutes but within 120 seconds the visitors were level when Marc Pugh fired on off the body of Howard.
It prompted a rise in tension levels at Goodison Park but the introduction of leading scorer Romelu Lukaku on the hour, replacing the ineffectual £13.5million January signing Oumar Niasse, marked a turning point.
Four minutes later Ross Barkley and Aaron Lennon combined to allow Leighton Baines to fire home at the far post for his first goal since November 2014.
Bournemouth have now lost five of their last six matches but with Premier League status already secured manager Eddie Howe can start planning for next season.
On the positive side striker Callum Wilson made his first start since rupturing his anterior cruciate ligament in his right knee in September and in the 79 minutes he was on the pitch looked lively.
"Callum did really well," said Howe.
"He has had a long period back
He was ready to start, played really well, assisted the goal and was a genuine threat.
"He can be very pleased with his comeback."
Source : PA
Source: PA