City have been on a great run since recovering from a slow start to the campaign, and won 2-1 in the FA Vase at Saltdean last Saturday.
But on Tuesday, they slumped to their heaviest league defeat of the season.
Horsham took the lead on 20 minutes when Tim Martin capitalised on a defensive mix-up and beat Matt Short.
Chichester struck back on 45 minutes when captain Michael Turvey rounded the keeper to equalise.
Turvey wasted a golden opportunity to give the home side the lead when he struck a post after again going past the goalkeeper.
George Hillier put Horsham back in front from close range and the visitors put the result beyond doubt when Lee Wood lobbed Short from outside the box.
City’s misery was compounded on 78 minutes when Hillier again took advantage of slack defending for his second.
The hosts began to lose their discipline and young midfielder Harry Gilbert saw red nine minutes from time.
Girdler believed his side made it too easy for their opponents. He said: “It was very disappointing. We should have come in 2-1 up at half-time. We played quite well first half. In the second half, for in the first 20 minutes we were the better side.
“Then Louis (Edwards) cost us by not tracking back for both their goals.
“Goals change games and we didn’t react to it, and our heads went down.
“We weren’t really at the races like we have been in the other games. But we’ve got to move forward and learn from it.
“Just because you have one defeat, it doesn’t make you a bad side.”
To add to City’s woes, defender Steve Cotton limped off with an injury in the second half and joins prolific frontman Ben Vassello in the treatment room.
Sent-off Gilbert will join suspended Joe Briggs on the sidelines and Girdler is feeling the pinch.
Girdler added: ‘We were missing a few personnel on Tuesday and two lads played with injuries, but we can’t make excuses from that. We have to get on with it – but it’s not helped.
‘The sending-off was disappointing, but as a bit harsh. They were kicking us all over the park. And Harry makes two challenges, and gets two yellow cards.”
On Saturday, Jack James and Josh Garvey got the goals that earns City a second qualifying round tie at Sidley this Saturday.