United slipped to their lowest-ever Premier League finish of seventh last term as they failed to adjust to life after Sir Alex Ferguson.
David Moyes was appointed as Ferguson's successor last summer, but he struggled to continue his Scottish compatriot's success as United lurched from one disaster to another under his guidance.
A string of unwanted records were racked up under Moyes, with Newcastle's 1-0 victory at Old Trafford back in December giving the Magpies their first win at the home of United since 1972.
Their 2-1 reverse against West Bromwich Albion in September was the Baggies' first away win at United since 1978 and Moyes failed to register a victory against Chelsea, Liverpool, Manchester City, Everton or Spurs before he was sacked in April.
Ryan Giggs took over as the interim boss for the final few weeks of the season but they eventually finished a whopping 22 points behind eventual champions, and fierce local rivals Manchester City.
Jones has accepted that the players cannot offer mitigating explanations as to why their performance dipped so badly from the 2012-2013 Premier League-winning campaign.
Speaking to the club's official website, the England international said: “As everyone knows last season was a difficult one for all of us involved at the club. It was nowhere near where we want to be and what we want to achieve.
"Yes there was a transition with the new manager but that’s no excuse – for whatever reason things didn’t happen on the pitch."
It's been a disappointing 12 months for Jones, and his poor domestic campaign was only worsened by England's insipid display at the World Cup.
Roy Hodgson's side lost their first two games against Italy and Uruguay, and their exit was already confirmed before their 0-0 draw with Costa Rica.
“The World Cup was disappointing for some of us too but that, and last season, only make you more determined to ensure we have a good season this time," added Jones. "We’re all raring to go and we know this is an important season for us. We’re under a new manager and really looking forward to getting going.”
However, despite the Red Devils' struggles last term, the versatile former Blackburn Rovers star believes that the side can shake off the disappointment to seriously challenge for the Premier League title under Louis van Gaal this coming campaign.
He said: "Of course everyone wants to win the title. It [being at the top] is where we belong as a club but we have no given right to say we should win the title every year.
"We have to go out there and do the business to win it ourselves. We can only do that by taking each game as it comes starting with Swansea.”
United have spent around £60 million so far on Ander Herrera and Luke Shaw, and they have been linked with a move for a number of central defenders, including Roma's Mehdi Benatia and Borussia Dortmund's World Cup winner Mats Hummels.