The Merseysiders have made an encouraging but unspectacular start under Martinez after their season-opening Premier League draw at Norwich was followed by a goalless home stalemate with West Brom.
Martinez's men showed plenty of endeavour and enterprise in their first home match but could not find a way to break the deadlock.
They created numerous chances but found Baggies' England goalkeeper Ben Foster in good form while Marouane Fellaini and Seamus Coleman both hit the woodwork late on.
Howard said: "It feels good. We dominated possession and got a clean sheet.
"We didn't win the game but we take the positives out of it.
"It is early yet. I think we played well in both games and were a bit unlucky, But that is the way it works.
"I think the performances have been good all along and as long as we put good performances together we will get the right results.
"I think there is a lot more possession now, a lot more encouragement to get on the ball, be positive.
"Everyone has bought into it, we are excited about it.
"As long as we can keep that defensive record nice and tidy we will give ourselves a good platform to go forward."
Howard had a relatively quiet day, only really called into action in the second half to keep out good efforts from James Morrison and Shane Long.
The 34-year-old American said of the clean sheet: "It's good but not just for me personally, for everyone at the back.
"It helps, second game of the season. They are hard to come by."
The build-up to the game for Everton had been overshadowed by speculation over the futures of key pair Fellaini and Leighton Baines.
Everton rejected a £28million joint bid for the duo as "derisory and insulting" and the matter has clearly irritated Martinez.
The Spaniard has criticised United boss David Moyes, his predecessor at Goodison, after the Scot suggested Everton should let Baines and Fellaini leave for the good of their careers.
But the affair clearly did not affect the performances of the two players, who were both prominent in a tight contest.
Fellaini had the best of numerous Everton chances when he deftly controlled a Phil Jagielka cross and stabbed against the post.
Foster had earlier denied Steven Pienaar, Kevin Mirallas, Ross Barkley and Coleman in an inspired display before leaving the field with an ankle injury.
His replacement Luke Daniels, the Baggies' third-choice keeper, also held firm although he had an escape when Coleman's cross-cum-shot hit the bar.
Howard said: "I think draws are always good if you can sneak a win in the run somewhere - you feel unbeaten, you're picking up points.
"Draws hurt you when you lose on the back of them, but at the moment we are positive."
West Brom created little in comparison but their display of resilience was encouraging after defeat in their opening game against Southampton.
Defender Billy Jones said: "It is always a hard game coming here.
"It was their first home game, they really wanted the three points and were really going for it.
"We are just happy as a team with the defensive performance we put in to get that point."
It had also been a difficult week at The Hawthorns with uncertainty surrounding the future of veteran striker and summer signing Nicolas Anelka.
Anelka has been granted indefinite compassionate leave following the death of his friend and agent but there have been suggestions he is considering retirement.
Jones said the squad were not disrupted by the matter.
The 30-year-old said: "We just know exactly what the club have informed everyone about. He has been given time away.
"Hopefully he'll come back but I have no inkling into what Nico is thinking.
"We worked really hard in training this week.
"We knew it was going to be tough and we wanted to put in a performance that shows what we are all about.
"I think we showed that and there is no better place to show it than Goodison Park."