The 27-year-old striker came on as a substitute for Gabriel Agbonlahor at the start of the second half of the Premier League game at White Hart Lane.
"I saw the ability of (Rudy) Gestede a few weeks ago at Anfield, and I was surprised he didn't start actually as he has done OK for them," Carragher told Sky Sports.
"We spoke about Gabriel Agbonlahor's lack of involvement and he (Gestede) was certainly more involved in this second half.”
Agbonlahor was hugely disappointing in the first half, managing just eight touches of the ball.
Gestede, who joined Villa from Championship side Blackburn Rovers in the summer transfer window, produced a much better performance.
The Benin international took three shots, had a pass accuracy of 47% and won 78% of the headers.
Villa lost the Premier League game against Tottenham 3-1 and remain at the foot of the table.
The Villans have picked up just four points from 11 matches and are four points behind 17th-place Bournemouth.
Villa will return to Premier League action on Sunday afternoon when they take on Manchester City at Villa Park.