Hodgson, who is now the head coach at West Brom, was sacked as Liverpool boss after six months in charge, after being appointed on a three-year contract.
Standing alone: Hodgson suffered during his ill-fated reign at Anfield
Speaking before the visit of his old club to The Hawthorns tomorrow, Hodgson said Dalglish's achievements loomed large over his tenure, and were made more pertinent by the fact he was appointed at the expense of the former Scottish international.
'It's difficult to compete with icons.
'I came to the right club, perhaps I didn't come at the right time because Kenny did make it clear at that time that he wanted the job.
'The people who were making the decisions at that time decided to go for me, and as a result that left Kenny in a difficult position because he is one who wanted the job.
'So when things didn't go well, having him in the background wasn't easy and wouldn't have been easy for any coach.'
All smiles: Liverpool's fortunes have been on the rise since Dalglish's arrival
However, Hodgson added this scenario was by no means exclusive to Liverpool.
He said: 'That happens at virtually every football club, to be quite honest. There's always someone in the wings who's a little bit of an icon and who's ready to take over if the results don't go that way.'
Hodgson was keen to stress his sole motivation ahead of the match lies with keeping West Brom in the Premier League, rather than proving a point to his previous employers.
'There is no vindication factor at all.
' enjoyed my time at Liverpool, well, I say I enjoyed my time, that would probably not be strictly true.
'I was treated correctly in every respect and by everyone at the club.
The former Fulham boss never had the full support of the fans at Liverpool, who made their disappointment clear from the terraces on a number of occasions.
Unison: Liverpool fans buoyed by Dalglish's return to replace Hodgson
For this reason, Hodgson said he is unsure of the reception he will get from the travelling supporters tomorrow.
He said: 'The reaction to my appointment from a large body of the fans was not positive so I don't know if that would have changed now I'm no longer there.
'Whatever the reaction is, we as managers have to accept that and get on with it.
'It would be nice if their response was not a negative one, but if it is, I'll have to learn to live with it.
'Hopefully the West Brom fans will will try to buoy me up in the other direction.'
Despite his torrid experience at Anfield, Hodgson has no regrets about taking the job.
'I still think that it was the right thing to do.
'I was realistic, I knew the risk when I went into the job.
'I'm still disappointed that it didn't work out in a better way, but I have no regrets and I have no bad feelings about Liverpool as a city, certainly I don't have any bad feelings about the football club and I have only good feelings about the people I work with there.'
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