Mauricio Pochettino's Spurs fought back from a goal down to grab a share of the points at Goodison Park with Dele Alli's lovely volley on the stroke of half-time cancelling out former Tottenham winger Aaron Lennon's earlier strike.
The result leaves Spurs in fourth place on the table but the fact they have only lost twice in 20 outings suggests to Carragher that they have the consistency to seriously push for a Champions League spot while potentially making their presence felt in the race for the premiership.
"I think Arsenal and Man City will battle it out [for the title] and [Tottenham are] an outside chance," said Carragher on Sky Sports.
"I think they'll be disappointed that they dropped two points, they're six points now behind Arsenal which is a decent gap halfway through a season.
"It's more the performance today that would give me great hope if I was a Spurs fan that they'd be part of the race.
"I think they'll be in the top four, I think they've got a top manager and a top group of players. They very rarely lose - they've only lost two games - and they're solid at the back, so I'd certainly say they'll be in the top four with an outside chance of the title."