Lacina Traore struck the only goal of the 1-0 win for Anzhi.
Rodgers felt the team, which contained nine Englishmen, a debutant in Conor Coady and had an average age of just under 24, had performed well.
"Not at all. I think that is a little disrespectful to the players who are here," said the Northern Irishman in relation to whether bringing Steven Gerrard and the others would have made a difference.
"They have been magnificent and I thought they did really well and we just got punished for a mistake.
"It was just one of those things. We will take it as a team, we are disappointed but there are so many positives."