Hull looked as though they might hang on for a point at one stage and even had opportunities to go ahead themselves at Goodison Park.
But, after having Tom Huddlestone sent off, they ended up well beaten, conceding late goals in a 4-0 loss.
Maguire thinks the scoreline was harsh and is now looking ahead to the next clash at home to West Ham in two weeks.,
He told the website: “Anybody who watched the game would probably agree that 4-0 wasn’t a reflection of our performance, but the sending off changed the game.
“We got punished for a slow start when we went 1-0 behind and the first half became a bit of a grind, but we came out in the second half and we were the better team.
“We had all of the ball, we were creating chances but then the decision to send Tom off changed the game. It’s hard enough against Everton when you have eleven men, but we’d managed to get some rhythm into our play before the red card.
“However, it was sloppy from ourselves after that because once Everton got the second goal we should have tightened up and seen the game out. They managed to cut us open several times towards the end of the game and the last two goals are goals that we should not be conceding. We only have ourselves to blame for that.
“We have to move on now and get our heads up because we have two very big home games coming up after the international break.”