Arsenal recently lost Hector Bellerin to injury as the fullback has been ruled out for up to nine months after rupturing his anterior cruciate ligament.
Arsenal fell to the Red Devils 3-1 in Friday's FA Cup clash with Lingard, Anthony Martial and Alexis Sanchez providing the goals for Manchester United in a match where the two key defensive pieces were forced out.
"I’m happy because I think our work is good, but the result is bad," Emery said after the loss.
"Today it’s the result and the injuries. They don’t help us to be in the match, maybe when the result’s 1-2. In this moment we had the possibility to grow and to win, but these injuries - especially the one to Koscielny - didn’t help us because our rhythm went down.
"Also, we needed to change different players to play at centre back. They were very clinical today and in the moments when we attacked, we got into the box but couldn’t produce the last action to score.
"We deserved more but we played against Manchester United who are in their best moment of the season, and they have a lot of players to make the difference."
On Friday, Koscielny was at the center of a collision with Romelu Lukaku, as the Manchester United forward's foot collided with the Frenchman's head.
Lukaku immediately signaled to the physio, ruling Koscielny out after a lengthy delay in play.
The incident came after Sokratis was also knocked out of the match after falling awkwardly on his ankle while competing for a ball against Jesse Lingard.
Sokratis was then replaced by Shkodran Mustafi in the 20th minute.
"I think they weren’t big injuries for Sokratis [his ankle]," Emery said after the match. "Maybe Laurent Koscielny is going to hospital to [analyse] what injury he has. Maybe he’s broken [his cheek or jaw] but I hope not.
Bellerin's recent injury sees him join Rob Holding and Danny Welbeck on the club's long-term injury list.
Fortunately for Unai Emery, midfielder Henrikh Mkhitaryan is nearing a return from a fractured metatarsal.
Next up for Arsenal is a match against Cardiff at the Emirates on Tuesday before an away match against Manchester City next Sunday.