Petr Cech said Arsenal were disappointed to lose against Manchester United despite "dominating the whole game".
The Gunners sit 12 points behind Premier League leaders Manchester City having played a game more following Saturday's 3-1 defeat at Emirates Stadium.
The loss was largely self-inflicted as mistakes from Laurent Koscielny and Shkodran Mustafi proved costly in the opening 11 minutes before David De Gea made a series of fine saves to frustrate the hosts.
Alexandre Lacazette put Arsenal back in the game, but the hosts were stung on the counter again when Lingard scored his second of the game to kill the contest.
Goalkeeper Petr Cech told Arsenal's official website: "The game was decided at the start with our two mistakes and they scored.
"We need to make sure that when we create chances in a big game we score and don't make mistakes.
"There are not many times you play United and you dominate the whole game, having so many chances, so this is positive, but we are disappointed.
"We played against Huddersfield and we were on the other side of it (winning 5-0 last Wednesday).
"We had a spell where we had four shots and everything went in, this time it was the opposite.
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