The Red Devils have fallen back from a second-place finish in the last campaign to be amongst the contenders for a top-four spot.
However, with Ole Gunnar Solskjaer being handed a three-year contract as manager, Jones thinks United can edge closer to winning their first title since 2013.
Jones said: "I don't think we're far away.
"I think obviously we had a poor start to the season. It's sort of like a story of two halves of the season, really.
"That [challenging for major trophies] is the vision for the players, for the staff, for the fans, everyone involved in this football club.
"It's a wonderful place to play football and that's where we want to get back to.
"We need to knuckle down. We need to play better than we did [against Watford], but we need to keep improving as a team.
"We've not got long left of the season now but let's see where we can go. Then we can recover well in the summer and have a good start to next season.
"I think the fans, the media, everyone can see what he [Solskjaer] has done and how he wants to play since he came, and I think we've shown that in quite a few games.
"It's positive and we're looking forward."