Arteta lauds Lewis-Skelly and Arsenal's courage in passing test of character. Ange laments Spurs' passivity.
The contrasting emotions were predictable after Arsenal sealed a double over their North London rivals.
Mikel Arteta delighting in his team coming through a big test of their resolve and Ange Postecoglou conceding his Spurs were not good enough.
The Gunners boss had relief as well as joy, having seen his side slip to a crushing League Cup semi-final defeat to Newcastle a week ago before Sunday's FA Cup exit and the hands of 10-man Man United.
"I'm very proud of the team," Arteta said. "I think we were sensational.
"It was a good test to see after two big performances not being rewarded in two different competitions they have to play the biggest game of the season for our people in those conditions. And it's a test of attitude...of what they're made of, how much courage we have.
"I think we showed it from minute one with and without the ball and fully deserved to win the game. We made our people very happy and very proud of the manner in which they have played today.
"These boys want more, they want to be tested and they deserve a lot of credit.
"The result gives us the chance to enjoy the moment and we are still [part of the title race] because there's so much to play for."
An assured display from Myles Lewis-Skelly at left back was one of the biggest plus points of a great night for the hosts.
The Arsenal boss said: "Seeing an 18-year-old up against [Dejan] Kukusevski and [Brennan] Johnson in a big London derby for the first time to perform with that composure, with that attitude, with that control emotionally - it's very rare to see."
Postoecoglou said: "We were way too passive. Allowed Arsenal to take control of the game and we paid the price for it. Second half was a little bit better but nowhere near good enough.
"It's not the way I want to play, to be sitting in there and allowing Arsenal to play to their tempo.
"There's no magic cure here. You've got to get up tomorrow and work hard and on Sunday [at Everton] go and battle and turn around our fortunes and our season.
"Our results and our form in the league has been nowhere near good enough and that needs to change. We were nowhere near the level we need to be in such a big game.
"We are an aggressive team with and without the ball. We've shown that seven days ago against Liverpool. Tonight, especially in that first 45 minutes, we were way too passive. We weren't good enough to deliver on a big day."
