De Zerbi says Brighton struggled due to a lack of squad depth.
"The effort was good, good enough to decide this game," he said. "We played a good first half, until the second goal we were in the game and then finish.
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"This moment without a lot of important players it is tough to create a chance to score.
"We played against Arsenal and they are top of the table. Especially in this condition then we can lose against Arsenal at home. We are sorry for ourselves and our fans.
"Maybe we will not close the gap, I don't know. This gap to close with Liverpool and Arsenal we are not in the condition to close this gap, especially with all our injured players.
"I don't know what the club wants to do (in the future). My problem is on the pitch, to improve my players and my team. The others things are not my business."