Wenger, who only spoke to TV reporters at Stamford Bridge and did not hold his routine pre-match news conference before a game, sent out his message in an email to supporters and later expanded on his thoughts in a written statement to the media.
Saturday's defeat in his 1,000th match in charge of the club was Arsenal F.C.'s joint-worst defeat in the Premier League era and their heaviest defeat in London since a 6-0 loss at West Ham United in 1960.
Wenger, who described the day as "a nightmare" repeated that he took full responsibility for the result, adding: "We have to think deeply about it because it is not the first time it has happened in this kind of game.
"It all went wrong and we failed completely on Saturday because we did not turn up with a performance."
He continued: "We are intelligent enough and care enough about the club to of course be disappointed.
"It looked like we missed the start of our game and were caught on the counter attack. We were caught on the break.
"After that of course the game became very long because down to 10 men, down to 3-0 it became of course an impossible task. You just wonder, 'OK let's finish it'
"When you have to attack with 10 men and you're down 3-0 you know you have more chances to concede another goal. That's what happened."
The result left Arsenal F.C.'s in fourth spot, seven points behind leaders Chelsea but with a game in hand.
They remain a place ahead of arch-rivals Tottenham Hotspur who beat Southampton 3-2 on Sunday to close to within six points of Arsenal F.C., having played one more match.
It was the third time this season that Arsenal F.C. have suffered a big loss against another top four side having been beaten 6-3 by Manchester City in December and thrashed 5-1 by Liverpool last month.
Wenger drew comparisons with the Liverpool defeat saying: "The common thing was that it was a 12.45 game and twice we were caught at the start.
"There's no rational explanation other than the quality of our opponents and that we were caught at the start of the game. Why We don't really know."
As well as the crushing loss, Arsenal F.C. also suffered the injustice of having the wrong player sent off when Kieran Gibbs was shown a red card by referee Andre Marriner rather than Alex Oxlade-Chamberlain who handled the ball in the penalty area.
Wenger added: "The sending off is simple.
"If the red card is rescinded we will have Oxlade-Chamberlain available" he said. "and because of the mistaken identity Gibbs should be available."
Swansea, who lost 3-2 at Everton on Saturday, travel to the Emirates having slipped close to the relegation zone after a poor run of form but will take heart from their surprise 2-0 win at Arsenal F.C. in the league last season.