"If we had been more consistent, we could have won the league," Monreal told the club's official website. "Unfortunately, a couple of months ago we had a slump and lost a lot of points. We lost our edge and the chance to go for the title.
"All things considered, it has not been a bad season but we are ending it with a bittersweet taste in our mouths. Our aim is to win, of course, so if we don't win anything, we have to be self-critical while remaining ambitious."
Asked about how Arsenal can go one better this season to earn a first title since 2004, Monreal replied: "Primarily we need to be more consistent.
"We are a team that is ambitious, that wants to win, that has a real hunger to win but we can change from one day to the next into a team that lacks those qualities.
"We must be more consistent and fight for everything from the first minute of the game until the last to ensure we get those three points. We have to improve.
"We've got a lot that's really good. We have quality players but at times we are a bit complacent and maybe do lack that hunger.
"The team is going from strength to strength. There is always room to improve further, of course. Since the day I arrived at Arsenal the squad is growing and has got steadily stronger.
"It is very competitive and that pushes up standards. We are on the way up.
Our biggest regret, of course, is not winning the title. It has been an a typical year. No one expected Leicester to achieve what they have.
"They have been the most consistent team in the League for the whole season.
"Inevitably we end up thinking that if only we had been more consistent, if only we had not dropped points in certain matches, we could have won the title, but things have turned out as they have."