United will be 15 points adrift of the top four by the time they face West Ham on Saturday evening if Arsenal and Manchester City win their games earlier in the day.
But at least United will go into the match full of confidence after they defied the odds to beat Olympiacos 3-0 and progress to the quarter-finals of the Champions League.
Jones thinks the 3-2 aggregate win was just what United needed after their defeat to Liverpool last weekend and the defender hopes the team will now be able to end the league season on a high.
"I think the Olympiacos game has got to be a springboard for us," the United defender said.
"It was a huge night. We have to use this as an impetus to go and prove that we can win game after game.
"We let ourselves down on Sunday so it was good to get the win for us and the fans.
"They have something to smile about now and hopefully we can kick on."
The win came on the back of a tough fortnight for Moyes.
The United boss was at a loss to explain his team's dismal 2-0 capitulation to Olympiacos in the first leg and the Scot then endured the pain of a humiliating 3-0 defeat to Liverpool last weekend.
Moyes had to face questions regarding his future after the Liverpool defeat, but Jones insists everyone is determined to help pull the team out of their current predicament in the league.
"We have all had criticism and we're in it together," the England centre-back said.
"We're a team, the manager and the staff, and we've got to band together and come through this difficult period, and we will do."
Olympiacos were considered the weakest side in the last 16 so United will have to greatly improve their performance over two legs if they are to make the semi-finals.
The line up for the last eight is one of the toughest in recent memory. Real Madrid, Barcelona, Atletico Madrid, Borussia Dortmund, Bayern Munich, Paris St Germain or Chelsea lie in wait in the next round, but Jones is not bothered who United draw.
"We're just happy to be in the next round," he added.
"Whoever we get we will welcome but hopefully we can go and put in another performance and qualify for the semi-finals.
"We left ourselves with a difficult task after the first leg but we came through the test with flying colours and we are excited about the next round."
The one downside to Wednesday's result was that hat-trick hero Robin van Persie was carried off on a stretcher with a knee injury.
Moyes said after the game that he hoped the injury was not serious and Jones echoed those sentiments, adding: "Hopefully he will be fit for Saturday and he can score a few more (at West Ham).
"He is terrific. He pops up with important goals in big matches and he did that again (against Olympiacos)."