There are still moves afoot to bring in a left-back for the new manager to be able to work with, but Paul says several more players are needed in the long term.
The majority of the squad are still training at Chadwell Heath and Paul admits: "We are plugging up holes and the the training ground is not busy.
And Trevor Brooking agrees: "There is no question that before the Reading game you would like two or three extra bodies, at the very least, because Rufus Brevett is out for three or four months and Steve Lomas for two months.
"They are big players in this division for us, and we are missing their experience badly."
Paul adds: "From a point sometime pre-season where we had 13 players, we are now up to about 16, and that is the football club.
"But in amongst them we have got some good players and we are having to rebuild the side from a day or two before Preston when Joe was sold.
"These are players that have only played together for four or five games, and it doesn't just happen that you start to get a focus in on how you are supposed to play with certain players.
"But we are working very hard at it, anyway."
With the transfer deadline as regards Premiership clubs having passed yesterday, following a day's extension, Paul is left to rue the change in rules which allowed two high profile players that may have been of interest to West Ham to move on loan within the Premiership.
"One thing that has hindered us is the fact that Premiership clubs can now loan to Premiership clubs whereas last year they couldn't," he says.
"For example Carlton Cole has gone to Charlton instead of a top first division side - which we would hope to consider ourselves as - because he was pushed out at Chelsea.
"Jermaine Pennant has gone to Leeds from Arsenal; those sort of players would definitely, last season, have filtered into the first division while this year they are staying in the Premiership.
"It is a massive blow even though it sounds like quite a simple rule change."
He does find it surprising, though, that the managers of the outgoing loanees have allowed it, and adds: "I must say if I was a Premiership manager I wouldn't loan one of my players to another Premiership club because of obvious consequences.
"Those managers have made that decision; I certainly wouldn't have done that but it is up to every individual.
"Maybe they feel that they won't get relegated, you just don't know, but obviously Carlton Cole has got to play against Chelsea and he might just get the goal that denies them the three points that in turn might deny them the championship.
"Then the decision might look a little bit strange, mightn't it?"