The Republican candidate was beaten by incumbent Democratic Senator Mark Kelly in a race called by the Associated Press on Friday night.
The win for Mr Kelly gave his party 49 Senate seats and needing just one more seat to secure a US Senate majority with Nevada and the Georgia run-off still in play.
Mr Masters was interviewed by right-wing host Tucker Carlson on Fox News and asked why Mr McConnell, the Senate minority leader, had “avoided” the Arizona race.
“I will leave it to the viewer to decide whether it is just malice or whether it is gross incompetence,” replied Mr Masters.
“But clearly Mitch McConnell cares about Mitch McConnell and less about his Senate majority or the people of America. I think we need a change, that’s why I ran for office and one way or another change is coming.”
Mr Masters on Saturday refused to concede the race saying that he wanted to “make sure that every legal vote is counted.”
“If, at the end, Senator Kelly has more of them than I do, then I will congratulate him on a hard-fought victory. But voters decide, not the media; let’s count the votes,” said Mr Masters.
Mr Kelly, a former astronaut, ran as a moderate Democrat and distanced himself from the White House on issues such as immigration.
“Thank you to the people of Arizona for re-electing me to the United States Senate,” Mr Kelly said in a statement.
“From day one, this campaign has been about the many Arizonans – Democrats, Independents, and Republicans – who believe in working together to tackle the significant challenges we face.”