Germany international Per Mertesacker received his marching orders in the 18th minute at the Emirates Stadium after he hauled down Diego Costa.
The controversial striker punished the Gunners minutes later after his close-range finish beat his former team-mate, Cech, in the Arsenal goal.
However, the 33-year-old goalkeeper, who has won the Premier League title on four previous occasions with Chelsea, refused to be downbeat following Arsenal’s title race setback.
“We are only three points off the lead and have Leicester and Southampton at home coming up,” Cech told Arsenal’s website.
“They are difficult games but if we can keep winning our games, we can go back to the top.”
Arsenal are three points behind surprise Premier League leaders Leicester City following Sunday’s 1-0 defeat by the west London side.
The Gunners’s London derby defeat was their first Premier League loss since an emphatic 4-0 reversal at St Mary’s on Boxing Day.
Arsene Wenger’s side welcome the Saints to the Emirates Stadium in their next Premier League game on Tuesday 2 February.
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