David De Gea's delight at Manchester United’s "massive" win in the race for Champions League qualification came with a warning that they are still not performing well enough to finish in the top four.

Last weekend’s embarrassing 1-0 loss at struggling Everton left the seventh-placed Red Devils six points off the pace and Ralf Rangnick admitting it would be "very difficult" to reach European football’s top table.

But the stars aligned on Saturday as Cristiano Ronaldo’s hat-trick spared United’s blushes and secured a 3-2 win against spirited Norwich as top-four rivals Tottenham and Arsenal suffered shock defeats.

Those results injected new life into the Red Devils’ hopes but De Gea is not getting ahead of himself after a poor display against the league’s worst side and Tuesday’s trip to title-chasing Liverpool looming large.

"Until the last second it was very stressful," the United goalkeeper said. "We were 2-0 up against Norwich so we cannot lose the control of the game.

"We started giving chances away, they score at the end of the first half so that’s always tough but I think we need to control more the games, especially at home against Norwich. But I think they played a great game.

"At the end we fight until the end, good spirit from the team and three great goals from Cristiano.

"It’s a massive three points. We’re still there fighting for the top four but for sure we need to keep improving because I think it’s not enough if we keep playing like this."

United had looked in cruise control after Ronaldo scored two first-half goals to a backdrop of protests against the Glazer family, only for Kieran Dowell to pull one back on the stroke of half-time.

Teemu Pukki stunned Old Trafford by levelling shortly after the restart and De Gea pulled off a fine save to deny Milot Rashica before Ronaldo thumped home a free-kick to seal a 3-2 win.

"This is the Premier League, it’s not easy," De Gea said. "Every game is tough.

"You see today against Norwich, bottom of the league, but they fight, they nearly get points here.

"It’s good for us if (our top-four rivals) drop points but, like I said, we need to keep improving, just focus on ourselves and keep winning games until the last one."

Tuesday could certainly provide a rude awakening if they put in a repeat performance at Anfield.

Liverpool head into the match buoyed by their 3-2 FA Cup semi-final win against Premier League leaders Manchester City and also won 5-0 at Old Trafford in October’s reverse fixture.

"It’s going to be a tough game for sure," De Gea told MUTV. "Always special to play against Liverpool, even away. It’s great to be there and play.

"Let’s see. We will go there and hopefully today give us confidence to go on Tuesday and play well, try to win the game and hopefully win the points for Manchester."