Defeat at home to Arsenal last Sunday leaves Spurs in 16th place on the Premier League table, four points away from the relegation zone.
The North London derby defeat marked Igor Tudor's first game in charge after the dismissal of Thomas Frank. However, despite the upheavel, Carr is convinced this Spurs team is too good to go down.
He told Tribalfootball.com: "Yeah, I'm confident, but I'm worried. I'm confident they'll stay up. But there's also in the back of my mind a little bit of a worry where they're at because the longer it goes, the pressure gets bigger.
"And then people's confidence drops by the game. So I am confident they'll get out, but it's not going to be easy. It's going to be tough. The next few games is big for them."
Asked why Tottenham have collapsed this season, Carr concedes he can't nail down any single reason.
He continued: "You can say the manager (Thomas Frank). With the manager, the players must perform to the highest level.
"The manager only does so much The manager sets it up all week. But it's about the team. When they go across that line they must perform.
"They've obviously had injuries, it's being highlighted. But you hate going on about it, because it's like making excuses. There's no team in that league that can cope with such an injury list. There's no one.
All these teams, the big boys and all, you take three players out of their team, they are not competing for the Premier League. And these teams have bigger depth in squad's of quality because they've been up there all the time.
"They can spend, they can get players, they can attract players. Tottenham have had key players out. But, as I say, it's not an excuse."
Steven Carr was speaking to Tribalfootball on behalf of Gambling.com where users find the best UK casino sites