The league leaders conceded an injury-time equaliser against Tottenham on Sunday, allowing Manchester City to close to the gap at the top of the table to just five points.
Sir Alex Ferguson's side let slip an eight-point lead at the backend of last season, but Jones insists United are capable of closing out the title race this time around.
"Confidence is high, but we know we still have to produce and do our job every time we step out there," the 20-year-old told The Mirror.
"As long as we're focused on what we've got to do and on our game-plan hopefully we'll be okay.
"This period is always tough with a lot of games in a short space of time, but now we're getting towards the nitty gritty part of the season.
"It's the time when you need to be fully aware of what you've got to do and make sure you do it.
"We all relish the challenge. Everyone is very focused and committed and we're ready for the next game."
The Red Devils face Fulham in the FA Cup on Saturday, a competition Jones is keen to do well in.
"The FA Cup is a great competition and one we want to win", Jones added.
"It's a competition I've always admired and we want to go as far as we can."