Martinez was sacked before the end of last season after a second successive disappointing campaign for the Blues.
They finished 11th in the table, a position far below where many felt they should be given the talent available in the current squad.
That came after they had finished 11th the season before too, a far cry from his first year in charge when they had nearly secured a Champions League place.
Ronald Koeman is now in charge at Goodison Park, and in praising his new manager Kenwright criticised the Spaniard.
“As you know, he [Koeman] is pragmatic because he is Dutch,” the Daily Star quotes him saying.
“Roberto was not pragmatic. You all laughed when I said he promised Champions League but he nearly did in that first season. I don’t think for one second Ronald has joined us and is not thinking of the Champions League.”
Attention now turns towards the work that Koeman will do in his first summer transfer window at the club.
If they do harbour desires of being a Champions League team, there will need to be significant improvement of the current playing squad if last season is anything to go by.
More importantly, he will need to try to retain star men such as Romelu Lukaku and John Stones, who have both been linked with big money moves elsewhere.