Daly took charge of the Hearts senior team for the first time having replaced the sacked Ian Cathro just four days before the start of the new campaign, and his side were swept aside by last season's treble winners at Celtic Park.
Before the match, Rodgers questioned whether the players who arrived at the club during Cathro's tenure were his own choices, prompting Daly to hit out at the "disgraceful" comments.
"It is absolutely disgraceful. I think it is very poor form. A manager of his calibre should know better. I followed Brendan's career when he was at Liverpool and never once did I hear him make a comment about Man United's structure, about Chelsea, about Man City's structure, but all of a sudden he comes to Celtic and he thinks it is acceptable to talk about the structure of our football club," he told reporters.
"Our club at the moment is very easy to pick on and kick, but for a manager of his calibre to come out and make the comments he did was unacceptable. I can understand the comments made about the manager leaving but once he starts talking about the recruitment of players, fitting into the system and questioning Ian's authority, it shows me he doesn't know Ian Cathro very well. There is no chance that any of those players that came in the door would have come in without Ian's say-so.
"Brendan is a knowledgeable man. The fact that he thinks Michael Smith, Kyle Lafferty, Christophe Berra, Rafal Grzelak, Connor Randall don't suit a 3-4-3 system baffles me. It really does. We have wing-backs, strikers, centre-back, combative midfielder, it is actually farcical that he thinks they didn't fit into that system and the fact that he thinks that other people around the club makes the calls and to comment on it is an absolute disgrace.
"Also, there were other comments - you've got me going here - and the fact that myself, Liam Fox, Austin MacPhee, Paul Gallacher are going to come here and play a basic shape, I think was the quote. What's the difference between a shape and a basic shape? Is there a difference? Does he play a basic 4-3-3? I haven't spoken to him but I will tell him when I see him that I am not happy."
Hearts will renew their search for a first win of the season away to Kilmarnock next Saturday.