Andre Villas-Boas felt his Tottenham side outplayed Arsenal, despite in the north London derby.
Emmanuel Adebayor put Spurs ahead before being sent off. Hosts Arsenal then took control to hand the visitors their third consecutive league defeat.
"I think we were on top from the first minute to the last," Villas-Boas told BBC Radio 5 live.
"The scoreline is big for Arsenal but the game wasn't so big. It was big on our side. We were unbelievable today."
Adebayor capped a fine start from Tottenham with the opening goal in the 10th minute, and Aaron Lennon came close to doubling the lead soon afterwards.
However, ex-Arsenal striker Adebayor then caught Santi Cazorla with a high and late challenge that earned him a straight red card on 17 minutes.
That shifted the momentum and Per Mertesacker headed the Gunners level before strikes from Lukas Podolski and Olivier Giroud.
Although Cazorla extended Arsenal's lead, Gareth Bale pulled one back and Spurs had more chances before Theo Walcott made it 5-2.
"With 10 men on a pitch like this it's very easy to do 20 passes when the clock is ticking down," said Villas-Boas.
"But it is not easy to do them when you are under pressure and you don't feel comfortable to play against an opponent with 10 men and being better than you.
"So I certainly compliment Arsenal for what they did, but we played with great passion, great ambition and desire. We are very proud."
Since their home victory over Aston Villa on 7 October, Tottenham have lost five of their six matches in domestic competitions.
Defeat sees the White Hart Lane club drop a place to eighth in the table, and they have still only won at Arsenal once in 19 years.
"We keep a smile on our faces because we were excellent for 90 minutes with 11 men and with 10 men," said Villas-Boas.
"I can't do anything but compliment them. When we went to three at the back the intention was to play good football with no fear whatsoever, with passion. The circumstances fell to Arsenal.
"We had a good opportunity to stun everybody. We take another defeat but we come out very proud of ourselves."
The Portuguese had no complaints about Adebayor's dismissal but added: "It was a pity for the game because it was being played very well by Tottenham."
For Arsenal, this was their first win in four matches and only a second victory in eight games in all competitions.
"I believe we have something special in our team," said boss Arsene Wenger, whose side rise to sixth.
"Our confidence has been knocked down a little bit recently but this result will help to play with full belief. We have a special spirit and we have shown that today.
"It was vital because in the modern world it goes so quickly from one extreme to the other that every bad result today has huge consequences on the mental environment.
"So it was important to win and it will strengthen our confidence."