Scot expects club to find out more about the pair at the beginning of next week while opposing manager Roy Hodgson fumes over penalty awarded to Luis Suarez in first half
Gerrard was a late omission for his side’s match against West Brom thanks to an infection which flared up on his ankle whilst Carragher had a strained calf.
Neither player was missed, though, as the Reds overcame the Baggies 2-0 at the Hawthorns thanks to a Charlie Adam penalty and an Andy Carroll strike.
When asked whether Gerrard could be fit to play for England next month, Dalglish said that he did not know, but he hopes to have a better idea when both will return at the start of next week.
“Carragher has a calf strain. Steven Gerrard has got an infection in his ankle. He was in our minds for the game, it just flared up,” he told reporters.
“We are off Sunday, we will be back in Monday or Tuesday, so we can be more accurate next week than we can be just now.
“We are certainly much better with them in the squad than not. They have been magnificent for this football club and they will continue to be so.
“I suppose it’s a reflection on the strength of the squad that we are without our two talismen and we still put on such a good performance.”
On the pitch, Liverpool put in an assured performance to see off the Baggies and push their unbeaten run to five matches.
The controversial moment of the match came early on when Luis Suarez won his side’s penalty after tumbling over from a challenge by Jerome Thomas.
But instead of being drawn on whether the correct decision had been made, Dalglish decided to praise his players for securing the three points.
“I thought we played really well, we thoroughly deserved to win the game and some of the football we played was fantastic,” he said.
“I’m going to sound like Arsene [Wenger], I never saw it [the penalty incident] from where I was standing and I haven’t seen any replays. I’m not trying to be evasive or duck the question.
“It could have been more comfortable but a 2-0 win was pretty satisfactory for us coming here. We knew it would be difficult for us. We played some great football and could have had a few more goals.
“The clean sheet is very pleasing but goals win you games.”
Dalglish’s opposite number Roy Hodgson held a different opinion on Liverpool’s penalty, which he clearly felt was a soft decision given by the linesman.
“I thought the referee like the rest of us saw it, didn’t see anything but the linesman did and the referee decided to take the linesman’s advice,” he told reporters.
“I doubt many people saw anything different to how I saw it – a situation where our defender is entitled to screen the ball to clear, should have been allowed to do so.
“I think we played as well today as we have been doing, but it would have been nice to have a chance to play at 0-0 for a longer period of time.
“You can do without having to play with a handicap.”
However, the former Liverpool manager was equally as scathing about his own side’s performance for the visitors' second goal as Carroll was given plenty of space to run through and slip his shot underneath Ben Foster.
“That was the worst thing, the second goal, that’s totally of our own making,” he added.
“We’re having a slightly better spell, we were taking the game to them, but of course we got caught with a lot of players forward, the ball got intercepted and we got caught on the counter-attack.
“We have no-one to blame but ourselves for that, that eventually of course meant that would could have been quite an exciting second half, at 2-0 you don’t get that situation."