Debutant Matthew Longstaff’s second half strike condemned Ole Gunnar Solskjaer’s men to their third league loss of the season in just eight games.
Manchester United’s start is the worst they have endured in 30 years with the club just two points above the relegation zone in 12th place.
Since beating Paris Saint Germain in the UEFA Champions League in March, United have failed to win a single away game in all competitions.
De Gea, who joined the club from Atletico Madrid in 2011, had also admitted this is the toughest period he has been in as a Manchester United player.
Asked what was missing from their performance against Newcastle, De Gea told Sky Sports: "Everything. A lot of things to improve. They were the better team today.
"I don't know what to say, really. Just keep trying, fighting, improving every day. It's a hard moment for us.
"It's probably the most difficult time since I've been here. I don't know why, what is happening. We cannot score even one goal in two games.
"It's difficult to say something. Sorry to the fans. We will keep fighting for sure, we will come back, but at the moment we are in a difficult situation.
"We defended quite well. It's true they had good chances to score but, come one, we conceded a goal from our corner. That cannot happen.
"It's not acceptable, not just this game, the whole season. Keep fighting and see what happens in the next games."
Things do not get easier for Manchester United after the international break as they host leaders Liverpool in their next Premier League game on October 20.