The Gunners were 5-1 winners against Everton at the Emirates Stadium in their last Premier League game before the north London derby.
Pierre-Emerick Aubameyang opened his Premier League account with a precise finish on his first Gunners appearance, while Henrikh Mkhitaryan made three assists in his home debut.
However, Arsenal were unable to trouble the Tottenham defence despite the addition of Aubameyang and Mkhitaryan in the January transfer window.
England international Harry Kane scored a first-half winner to secure a 1-0 win against Arsenal in the derby clash at Wembley on Saturday afternoon.
Arsenal are eight points behind fourth-placed Chelsea FC with 11 games to go in the 2017-18 Premier League campaign.
Former Liverpool FC defender Carragher emphatically ruled out Arsenal securing a top-four spot and a return to the Champions League.
“I think it’s virtually impossible for them [to finish in the top four] because they’re not catching Man United,” Carragher said on Sky Sports’ Monday Night Football.
“It’s very difficult to catch Liverpool because of the points gap and because they’ve got two winnable home games. Arsenal’s next game is Man City.
“Tottenham are the best team in the league in the second half of the season. And the biggest reason is they’re not good enough. That’s it. They’ve got a points deficit and they’re not as good as any of those sides.”
Arsenal finished in fifth place in the Premier League table last season to miss out on a spot in the Champions League for the first time under Arsene Wenger.
The Gunners will face runaway Premier League leaders Manchester City in the League Cup final at Wembley later this month after a 2-1 win against Chelsea FC in the last four.
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