Palace have registered just five top-flight wins in a season blighted by injury and travel to title contenders Arsenal on Saturday sitting five points above the relegation zone.
Eagles boss Hodgson was subjected to chants of ‘you don’t know what you’re doing’ from unhappy away supporters after substituting Eze during the midweek FA Cup third-round replay loss at Everton.
Eze and Olise, who remains sidelined ahead of the visit to the Emirates Stadium due to a hamstring issue, have started alongside each other only three times this campaign.
Former England manager Hodgson is confident the club’s predicament will improve when the injuries ease and is hopeful of strengthening his depleted squad with a couple of January signings.
‘Unfortunately the way things have gone, it’s become a bit harder for us,’ said the 76-year-old, who began the campaign with the minimum objective of a mid-table finish.
‘But if we can maybe get a couple of those players that we would really like to have, when people like Michael and Eberechi start playing together, which to be frank they haven’t done very often, when and if we can keep that group together, we will start to the climb the table, that’s for sure.
‘But there’s a lot of work to do on the training field and with the players because it’s so easy to say the things I’m saying but it’s all about what you do on the field of play – that’s where the proof of the pudding will be.
‘But I believe that we’ve got players who will help us climb the table and then we’ll see how high we can get.”
Hodgson withdrew England international Eze, who has battled hamstring and ankle problems this season, at Goodison Park in order to protect him for the game against the Gunners.
In addition to Olise, he is also currently without Jesurun Rak-Sakyi, Rob Holding, Joel Ward and long-term absentee Cheick Doucoure, while Jordan Ayew is at the Africa Cup of Nations with Ghana.
‘The fans have been with the club a long time, they’ve seen the trials and the tribulations,” continued Hodgson.
‘I’m certain they dream one day that there will be no more trials and tribulations but they’re used to helping the team get through these periods of time.
‘I think we’re going to give them a little bit more cheer in the second half of the season, if we get players back and we start playing in a way we know we can play.
‘I know they’ll stick with us and will be cheering the team on and pushing us forward, but it’s up to us to give them something to cheer about.’
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