Gerrard, Cole and fellow England World Cup players Jamie Carragher and Glen Johnson were among the notable absentees for the third qualifying round first leg against FK Rabotnicki having only recently returned to training.
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Hodgson said: ''We were never close to that because they have only been training for four days.
''It would have been folly to try to play 90 minutes' football in an important competition in difficult conditions with players who have only been training for four days.
''We have pressed one or two players into service who were back one or two days earlier than that but in an ideal world we would not have used any of the players that played in the World Cup.
''But, quite frankly, we are not in a strong enough position to do that.''
Javier Mascherano and Maxi Rodriguez, who returned to training this week, were also missing while Fernando Torres, Jose Reina, Ryan Babel and Dirk Kuyt are still on holiday.
The match, coming 17 days before the club's Premier League opener, has presented Hodgson with a difficult situation.
Hodgson, who guided Fulham to the final last season after entering at the same stage, has to try to guide his side through while relying on inexperienced players.
The likes of Diego Cavalieri, Martin Kelly and Jay Spearing are all likely to get an opportunity.
The 62 year-old said: ''All competitions are important to the season. It's the first competitive game I have been able to have with the club.
''It would have been nice if the game was played later and we were able to play what we feel is our strongest team but we can't.
''But it is still a very important game and I hope the players we will give the confidence to play in this game and represent Liverpool will be able to do a good job.''