Meireles was Hodgson's first signing when he took over at Anfield before the beginning of the season, but the £11.5million had been a long-term Liverpool target.
The 27-year-old thinks that he did not enjoy the complete backing of his ex-manager, but that has been transformed since Kenny Dalglish was named boss in January.
Meireles said in The People: "It is certain that under Dalglish I get more chances than I did in Hodgson's time.
"I don't know why, but perhaps Hodgson didn't think too well of me. But I am the same now as I was then.
"The system we play now is different. We play more in attack, which helps me.
"Kenny Dalglish is closer to the players and he also speaks to them a lot more in training. The relationship between the players and coach is more direct.
"Hodgson is a veteran coach, an old-school gentleman, and was respectful towards the players. But the injuries and bad start to the season damaged our work with him.
"The key was to win the first few matches, which would have increased the squad's morale."