Enzo Maresca’s side were down to ten men after just five minutes when goalkeeper Robert Sanchez picked up a straight red card for a rash tackle on Bryan Mbeumo.
United captain Bruno Fernandes gave the home side the lead before Casemiro made it 2-0 in the 37th minute.
The Brazilian was then sent off just before half-time, but despite a late goal from Chalobah, 26, United held on to win 2-1.
Speaking after the game, Chalobah was remarkably honest about the result, suggesting that Chelsea players can no longer hide behind their young age.
“We have to look at ourselves as players. It wasn’t good enough for ourselves, for the club. The first 15 minutes is the worst we’ve played this season. We have to reflect on that as a team and learn from this,” Chalobah told Sky Sports
“With the red card that happens, you go 2-0 down in the game, any team you play against, it’s always difficult coming back. We struggled in the first half.
“It’s always difficult going down to 10 men and you can see that United were up for it. They put us under pressure. It wasn’t good enough at our end. We couldn’t get going in the first half.
“Things like this happen in the season. We can’t say we’re kids anymore, we’ve played in the Premier League long enough now. We have just got to learn from this and move forward.”