Carragher said: "It's the manner in which we conceded a goal at the end which hurts. When you score in the last minute it's the best feeling you can have, but when you concede, it feels like a defeat.
"We needed those three points to close the gap and get further up the table so we've missed a good opportunity. We had enough chances to win the game well before they scored.
"Liverpool is a big club and we've got to be challenging for the title. No matter what's happened so far this season, I think everyone knows we're still short of players.
"Even though we beat Arsenal, I don't think any of us was thinking that meant we had a squad which is good enough to challenge for the title.
"I'm not talking necessarily about replacing individuals, but more about getting numbers in. We need a bigger squad. We've lost a lot of players during the summer who still haven't been replaced, and while it's not an excuse, that's been seen with the number of injuries we've had. There are still a lot of players out now.
"Michael Owen hasn't been replaced and we lost Steven Gerrard for a long time. He hardly missed a game last season. It's no secret the manager is looking to strengthen in January so we'll get stronger."