Louis Van Gaal tipped his Manchester United side for a top four finish after Matteo Darmian's stunning strike helped maintain the push for Champions League football as fellow FA Cup semi-finalists Crystal Palace were swatted aside.
Van Gaal admitted United must win their last four games to have any chance of success.
"We are putting the pressure on," he said as fifth placed United moved to within a point of Arsenal and two of Manchester City.
"Towards the end of the season it counts much more and I am very happy.
"We have four matches to go and if we win them all we have a chance.
"We have to look at ourselves and not at our competitors."
United and Palace could do battle once again on May 21 if they navigate their way through this weekend's Wembley encounters - against Everton and Watford respectively - matches that offer both teams the chance to end frustrating seasons with a shot at silverware.
Palace's seven changes showed how much of Alan Pardew's focus was on their semi-final against Watford and led to an unsurprising outcome at Old Trafford, where United triumphed 2-0 as Darmian created one and scored the other.
The Italy international has struggled at times during his maiden season in English football but made an impressive impact last night, with his fourth-minute cross forcing Damien Delaney to turn past his own goalkeeper.
Julian Speroni could not prevent the own goal but did well to keep the score respectable on his first Palace appearance of the season, with Darmian needing to produce a moment of magic to beat him in the second half.
The stunning left-footed strike hit the post on its way in, wrapping up the win.
Darmian got United off to a flyer when he broke free down the left and sent in a cross that Delaney connected with, directing it low and hard past Speroni.
Juan Mata tried his luck with a low drive and Anthony Martial forced an acrobatic save as United attacked with unusual panache, before Wayne Rooney stung the palms of Speroni.
A wayward Emmanuel Adebayor shot was the only effort of note Palace could muster during a half in which the majority of play was at the other end.
Impressive pressing from Marcus Rashford resulted in Mata getting in a shot Speroni did well to tip wide, but the Palace goalkeeper could do nothing to prevent Darmian opening his United account in style.
The full-back hit an exquisite strike from the edge of the box that went in off the post.
It was an impressive goal that Rooney tried to add to with dipping effort, before Lingard and Rashford were then denied by Speroni in quick succession.
Palace boss Pardew said: "We worked hard but maybe our focus was on the cup."
Man Utd: De Gea, Valencia, Smalling, Blind, Darmian, Schneiderlin, Lingard (Ander Herrera 73), Mata, Rooney (Fellaini 78), Martial, Rashford (Depay 64).
Subs Not Used: Rojo,Young, Romero, Fosu-Mensah.
Goals: Delaney 4 og, Darmian 55.
Crystal Palace: Speroni, Kelly, Mariappa, Delaney, Souare, Cabaye (McArthur 66), Jedinak, Zaha, Lee (Mutch 60),Sako, Adebayor (Wickham 75).
Subs Not Used: Campbell, McCarthy, Puncheon, Dreher.
Booked: Kelly, Souare.
Referee: Lee Mason (Lancashire).