The Spain international was at fault for the opening goal, dropping a catch that allowed Ismaila Sarr to score his first Premier League goal for the Hornets.
Solskjaer spoke to Sky Sports (h/t AFP) after the match and refused to blame his goalkeeper but did add that his team did not deserve anything from the match after putting in a limp display:
"It was a mistake, it happens in football and it is what we train for every day to make sure they don't happen again. David has been very good lately, it is just one of those things that happen. You have to earn every point on the pitch and today we didn't deserve that."
De Gea's mistake is not the first he has made for Manchester United in the last two seasons:
Bleacher Report's Rob Blanchette said it was De Gea's worst mistake in a Manchester United shirt:
Watford went on to double their lead four minutes later from the penalty spot after another defensive mistake by the Red Devils.
Right-back Aaron Wan-Bissaka conceded a penalty with a clumsy foul on Sarr, allowing Troy Deeney to beat De Gea with his spot-kick and seal a first home win of the season for the struggling Hornets.
Solskjaer felt losing two goals in four minutes was too much for his side:
Sky Sports Premier League @SkySportsPL
"We started slow. When you concede two goals like we did in quick succession, we gave ourselves too much to do." Ole Gunnar Solskjaer speaks to Sky Sports after Man United's loss at Watford. Watch Super Sunday on Sky Sports PL now 📺 or follow here 📲https://t.co/PKd1XxlRa2 https://t.co/VPpqy5v63u
The defeat is Manchester United's fifth in the league this season and leaves them in eighth place, their lowest position at Christmas for 20 years:
Solskjaer's side return to action on Boxing Day at home to Newcastle United who have won three of their last four games and are level on points with the Red Devils in the table.