The Red Devils finished 19 points adrift of the reigning Premier League champions last season, with those at the Etihad Stadium securing the top-flight crown in some style.
Jose Mourinho endured a frustrating summer in his efforts to move his side closer to City, with a lack of movement in the transfer market doing little to enhance the depth of talent at Old Trafford.
United have, however, made a winning start to their 2018-19 campaign and Jones believes that they will be in the mix for top honours if they avoid getting distracted by the exploits of others.
“It’s the most difficult to win out of the competitions in England. The level of the players and their fitness and ability is improving.
“I remember when I joined in 2011; the Premier League has come on leaps and bounds since then – the pace of the Premier League and the games we’re playing in are so quick nowadays.
“You have to adjust and adapt to that, but it’s great to be a part of.
“The top six look very good and are going to be very competitive, so it’s going to be tough for us again this season – we know that – but I think we just need to focus on us a bit more and concentrate on how we’re going to approach games and let’s see where it takes us.”
Mourinho’s men opened the season with a 2-1 victory at home to Leicester, with Paul Pogba and Luke Shaw among the goals.
Their next outing is set to take them to Brighton on Sunday, with the Red Devils seeking to gain early momentum as they chase down a first title triumph since 2013.