The Reds are currently four points behind Spurs, who are fifth but have two games in hand.
The teams are set to meet at Anfield on May 15, by which time the Liverpool skipper — who showed no ill effects yesterday after being knocked unconscious following a clash of heads with youngster John Flanagan during the 1-1 draw with Arsenal on Sunday — hopes the gap will have been slowly chipped away.
“There have been a few times where we thought we can catch Spurs, then a couple of times when we lose a game that we can’t — now after these last two games we probably think we can,” said Carragher.
“We have now got two home games to come, but the best thing is not to worry about Tottenham and just worry about ourselves, then see at the end of the season where we come.”
Youngsters Jay Spearing and Flanagan both started again at the Emirates, while 17-year-old Jack Robinson came off the bench to replace injured full-back Fabio Aurelio.
England U19 midfielder Jonjo Shelvey also made an appearance, all of which left veteran Carragher, 33, in no doubt his club’s future was in safe hands.
“Having all these young players is great testament to them and the work done down at the academy, as well as the manager for giving them a chance,” said Carragher, who has made more than 600 appearances for the club.
“To achieve what we have in the past two games with all the injuries and having to play the young lads bodes really well for the future this season and next.”
Arsenal have found themselves under the spotlight again as Arsene Wenger’s men battle to end a six-year trophy drought.
Carragher, though, feels that criticism is unfair given the financial muscle of Arsenal’s rivals.
“There is so much competition up at the top — you look at the money [Manchester] City have spent and Arsenal are still the main challengers to Manchester United,” the former England defender said.
“Chelsea won the double last season, and again Arsenal are still the biggest challengers.
“The criticism Arsenal have been getting over the past few years for not winning anything is a bit harsh — you forget the money these other teams have spent compared to Arsenal.”