Spurs finished above their north London rivals in the Premier League last season for the first time since 1995.
But cracks are already beginning to show at Tottenham, despite their second-place finish in May.
Danny Rose has spoken out on the frustrations over low wages and a lack of new signings at the club.
And Mauricio Pochettino’s side face the tough adaptation from the comforts of White Hart Lane to life at Wembley this term.
Arsenal know full well how moving into a new stadium can take time, shown by their Emirates switch.
Spurs’ other London rivals West Ham also endured difficulties on and off the pitch at the London Stadium last season.
But ex-Tottenham midfielder Jenas, a BT Sport pundit, insists Daniel Levy, Pochettino and the Spurs players won’t be able to justify failure at Wembley or beyond.
“I don’t think they’ve got the room for excuses, I really don’t,” Jenas told Starsport.
“They’ve invested so much to be looked at as a certain type of club.
“And also obviously that battle of north London, people want to shy away from it or not talk about it but it’s right there for the first time ever.
“Spurs have almost got their foot on Arsenal. It’s a matter of going ‘stay there’ right now and not allowing them to come back because they will come back.
“They’re an unbelievable football club that won’t accept anything less than Champions League football themselves as they’ve proved over 20 odd years.”
On the new season for Spurs, Jenas added: “I don’t think any excuses will go down well anyway.
“Everybody knows they’ve got to play on this pitch.
“Then they move back into the new stadium. What, are we going to say it the year after? ‘Oh we’ve got a new stadium.’ No.
“It’s an issue, I don’t think its an excuse.”
Tottenham's first league game at Wembley comes 'at home' to champions Chelsea on Sunday (4pm).
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