The Birmingham Mail says the Baggies tried to bring in a defender on the final day of the window - Nedum Onuoha (Manchester City) and Chris Baird (Fulham) were late targets - but neither materialised.
Regarding that late pursuit, Hodgson said: "We were quite close. Dan worked very hard but unfortunately one of the players who we had an agreement with a club for decided at the last minute that he didn't want to make the move.
"That would have been the ideal transfer window if that situation had come about and you don't ever get the ideal.
"But it's been a successful window for the club, without spending a lot of money we have improved the squad and the team and given ourselves a better chance of survival."