The former Sunderland star made the comments following the Black Cats’ 6-2 defeat to Everton away from home at Goodison Park in the Premier League on Sunday.
“I remember staying up by a single goal when I was at Wigan in 2007, so clearly that could be crucial in the end,” Kilbane told BBC Sport.
“Big Sam has got time on his hands, and a transfer window coming up, but he has to find a way to stop his side shipping goals.
“I am sure he will invest in that area of his team in January, because if they carry on defending like this, they are down - it is as simple as that.”
Sunderland are second from bottom in the Premier League table at the moment with just six points from 11 matches.
The Black Cats have conceded as many as 25 league goals so far this season - more than any other Premier League team.
It is clear that the current Sunderland defenders are not good enough, and Allardyce will need to invest in January.
The former West Ham United manager should be given money to sign the players he wants to in order to keep the Black Cats in the Premier League next season.
Sunderland are back in action on Saturday afternoon when they take on Southampton at the Stadium of Light in the league.