Manchester United progressed to the quarterfinals of the FA Cup with a 1-0 win over West Ham United at Old Trafford on Tuesday. After a goalless 90 minutes, Scott McTominay scored the game's only goal in extra time to send the Red Devils through to the next round.
Maguire told MUTV that he felt his side deserved the win and a place in the next round.
"Yeah, we got there in the end and I feel we deserved it," the Manchester United captain said.
"We felt comfortable on the pitch, I felt in the first half we played with intensity and dominated the game, played the game in their half and had chances where we should be one, two, three up."
The England international also said that he was proud of the defensive record that his team have maintained in recent weeks.
"It’s massive. I think we have six in 10 games, if I’m right off the top of my head," he said.
"When we’ve conceded, we’ve conceded too many, when we concede one it seems to be two. It was three against Everton. That’s not good enough for this club.
"We were disappointed at the weekend, we felt we deserved the three points but we couldn’t feel sorry for ourselves. We knew we had to come here tonight and bounce back and get that momentum back on our side ready for Sunday," Maguire continued.
Harry Maguire says it was disappointing for Manchester United to lose in the semifinals last season
Since he was appointed as Manchester United captain last season, Maguire has seen his side lose four semifinals. That is a record he is determined to change this season.
"Last season, it was disappointing to lose in the semi-finals like we did, but we've got to win trophies. We've got to demand that of each other. We do. We demand that we win trophies and it’s vital the team starts winning trophies, for the club and the fans as well," he said.
With the quarterfinal draw happening on Thursday night, Maguire said that he was not bothered by the opponents' identity.
"We fancy our chances against anyone, we just need to look after ourselves, perform well and assure that we start winning trophies at this club," he concluded.