The Reds boss, who left the likes of Steven Gerrard and Luis Suarez at home, went down to Lacina Traore's sublime late first-half goal in Moscow.
However, Rodgers felt his young team, which contained nine Englishmen and a debutant in Conor Coady, held their own against Guus Hiddink's more experienced outfit.
"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 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.
"That led to us losing the game but I don't think it was anything to do with Suarez, Gerrard, Joe Allen, Martin Skrtel or Daniel Agger not being here.
"It was just one of those things. We will take it as a team, we are disappointed but there are so many positives from tonight.
"We are disappointed with the result. I thought the players put everything into the game."
With the team having an average age of just under 24, Rodgers praised his young stars and believes the experience will benefit them in the future.
He added: "Tactically our concentration was very good. We controlled the game for 44 minutes and 50 seconds of the first half
"We made a bad mistake and got punished and that is the level.
"Some of the young players were terrific and we are disappointed not to have got something from it.
"I thought the performance level was good on a difficult pitch but I thought the players played the system tactically very well.
"We just find ourselves unfortunate not to get something from a very difficult place."
Anzhi manager Guus Hiddink was happy to gain revenge for their defeat at Anfield a fortnight ago.
"They had a young side but that does not mean they were not experienced as some of those players play frequently in the Premier League," he said.
"They were good players, skilful players who were tactically good.
"They tested us but we also have some young players so it's a good result for us.
"We didn't finish it off in the second half, we had two big opportunities, but it was an interesting game on a very bad pitch.
"They tested us so we have to be happy with this result."