Wenger's only signings ahead of Sunday's match were the free transfers of Yaya Sanogo and Mathieu Flamini, while Spurs had shelled out a reported B£100million on new talent - with £26million man Erik Lamela among their substitutes following his transfer from Roma.
"Spurs spent a lot of money this summer, and were expecting to win, so I think that gave us an extra bit of determination to go out there and win the game, which we did," the Wales midfielder said.
"This shows we have a lot of quality in the team, that the manager believes in us, it shows that we believe in what we are capable of doing, to produce great performances.
"We know we have the quality in this team to do well and play, and beat anybody on our day - which we showed again against Tottenham.
"We had to dig in for large periods of the second half, but it was a good team performance and we deserved the win in the end."
The 21-year-old feels Arsenal's display showed they have the character needed to get a result when it matters.
"In the last five minutes, they were going to chuck everyone forward, it was more of a war than a football match. We really showed the grit and determination in this squad to succeed," said Jenkinson, a lifelong Arsenal fan.
"They have spent a lot of money, we know that, but at the end of the day, we did the job that we needed to do and came out on top. Long may that continue.
"I think (we did prove a point). Of course there has been a lot of talk around Spurs and the money they have spent, the players they have brought in.
"But we just needed to focus on ourselves, to go out and show what good players we have, how we can play when we are on top of our game. I think we did that."
- Sports & Recreation
- Yaya Sanogo
- Mathieu Flamini
- Erik Lamela
- Olivier Giroud