Carroll has only just returned from a two-month lay-off with a thigh injury, with Thursday's night's 0-0 draw against Braga being his first start since moving to Merseyside from Newcastle in a £35 million transfer.
Dalglish believes it is too soon for Carroll to be linking up with the natonal side, and he would be better off remaining at the club's training ground as he is nursed back to full fitness.
Dalglish said: "England have to be responsible with him. There is nothing we can do to stop them picking him but common sense has to prevail. It is not a case of going to war with anyone.
"I don't know if Fabio wants to pick him or not. But there is no point in us being as guarded as we have been in his recuperation and doing such a good job to get him to where he is now if someone else is going to waste all that.
"We fully understand somebody wanting to pick his best players for England but they also have to understand the fact that he is not really there yet for fitness. But if he picks him, he picks him. That's up to the England manager."
Meanwhile, Dalglish insists the club's European exit will not make him reassess their methods as they prepare for the first of nine crucial matches in the Premier League.
"Every game in the Premier League is different so there is no one correct way of doing something," he said. "Every team have their particular things they are good at and we have ours. We just have to prepare to try to nullify what they have got and get the best out of what you have got.
"I don't think we have done any different since we came in. We have tried to get the best out of the players we have here and against Braga they couldn't be faulted for effort."