The Red Devils were expected to mount a title challenge under Jose Mourinho this season but they settled for sixth place and put their focus into the Europa League in the closing stages of the term.
United’s failure to finish in the top four has been played down by most at the club after they secured a double with the Europa League crown and EFL Cup.
Jones feels it bodes well for next season as they look to compete on every front and he insists they won’t fear any opposition they may face in the Champions League or domestically.
"There is no doubt that when everyone is fit and everyone is playing well and confident we can take on anyone," Jones told ManUtd.com.
"We’re not scared of anyone and we don’t look at other clubs and think we’re miles away from them, far from it. But we know we can certainly challenge better than we have done this season in the league.
"It’s been tough at times, especially at home when we’ve created loads of chances but there has been some goalkeeping heroics or we’ve made the wrong pass at the key time, but ultimately I think we’ve had a good season."
Jones will be hoping to earn regular football next season with plenty of games to be played and punters may be tempted to use their free bet to back the Red Devils to challenge more seriously for the Premier League title.