The reaction angered Villa boss Martin O'Neill, but midfielder Sidwell says: "It's not often you hear boos at half-time at this stage of the season but, taking into account the end of last season, we have only won two games in 18 and the fans want to see better.
"They pay good money to come and be entertained and if they feel they are not getting that then they have every right to show their feelings."
The former Reading star believes a win at Anfield could still kick-start Villa's season.
"It is not nice for a player to come off at half-time or full-time and then get booed by your own fans - especially not just 45 minutes in," he said. "You want them to be getting behind you but they pay very hard-earned money and have got their own opinions. If they feel that is what we deserve, that is up to them."