Robin van Persie lifted the gloom at Old Trafford by scoring a hat-trick as United overcame a two-goal first-leg deficit by beating Olympiacos 3-0 in the UEFA Champions League on Wednesday to progress to the quarter-finals.
A 3-0 home defeat in the top flight against fierce rivals Liverpool on Sunday had raised more questions over the future of manager David Moyes, so the fightback against the Greek champions was a much-needed tonic for the Scotsman.
Seventh-placed United now turn their attention back to a disappointing Premier League campaign as they attempt to make up ground on the teams above them, and Jones is eager to build momentum for the remainder of the campaign - starting with Saturday's trip to Upton Park.
The England defender said: "I think the Olympiacos game has got to be a springboard for us.
"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 (against Liverpool) 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."
United have won their last two league games on their travels and not conceded in three on the road, but they will have to do without captain Nemanja Vidic as he starts a two-match ban following his red card against Liverpool.
Van Persie's fitness will be assessed after he was carried off late on against Olympiacos with a knee injury.
Defenders Chris Smalling (hamstring) and Jonny Evans (groin) are expected to miss out once again.
West Ham are due a win against United in the top flight at Upton Park as you have to go back to 2007 for the last time they secured a home win over the champions.
Moyes' men consigned the London club to a 3-1 defeat when the two sides met at Old Trafford back in December and Sam Allardyce's charges go into the game on the back of defeats at Everton and Stoke City.
West Ham have won their last three home games though, and Allardyce believes they need at least another seven points to be guaranteed safety as they sit six points ahead of third-bottom Sunderland but Gus Poyet's side have two games in hand.
When asked how many points will be needed to avoid the drop, the former Newcastle United manager said: "I think probably about 38. Then again, with nine games to go, some have 10, it's swings and roundabouts more than ever before."
Defender Joey O'Brien (dislocated shoulder) and striker Marco Borriello (calf) will play no part for the home side.
