He did and he didn't in my opinion.
Moyes used to struggle against United, Arsenal, Chelsea and Liverpool. He regularly beat City (home and away) which is something Martinez has yet to do in a league game.
Other than winning at Old Trafford in the same period as Newcastle and West Brom (when I think they lost over one hundred years of unbeaten home records against three teams in four home games!) and battering Arsenal 3-0 at Goodison (both in his first season), what else has he done to rid us of this mentality?
In the two seasons since, apart from beating Chelsea at home which is something all-comers were doing, we have done nothing in the league against United, Arsenal, Liverpool, Spurs or City.
Moreover, he is now lauding as "incredibly satisfying" away draws at hopelessly out of form sides such as Watford and Crystal Palace.
This has arguably returned us deeper into "plucky" territory than we ever were under Moyes.