Azpilicueta admitted the early goals were particularly damaging.
"We did not start very well because we knew they could have a reaction in the stadium with a new manager but we didn't cope well enough," said the Spaniard.
"We should have done much better in a game like this. In the first five minutes we gave away a goal from a cross, which we knew they were dangerous from, and after that we were in trouble.
"We conceded again early in the second half and in those key moments we weren't strong enough to cope with them."
Coping in adversity was a theme the 30-year-old returned to when discussing the reasons behind the setback.
"The mentality is very important and performing every few days is key to being a top team," continued Azpilicueta. "We lacked this mentality today to come here and fight, to be at our best against a team that were struggling.
"We were coming from a very good game against Aston Villa but we didn't show ourselves to be mentally strong enough to cope with this."