"Before the game we wanted to come here and beat Luton and we should be beating them," Carragher told liverpoolfc.tv after their 1-1 draw.
"But after the 90 minutes we're delighted to still be in the cup. We didn't play too well and if anyone deserved to win it was Luton. We accept that.
"We would have liked a better result because we are the favourites to go through."
Following a pulsating 5-3 win against the Hatters at the same stage two years ago, Carragher insists Liverpool knew they were always in for tough contest and believes a number of cup shocks over the weekend prove that, on their day, sides from the lower divisions can still match the giants of the Premier League.
"Luton is a tough place to come," he said.
"We knew that from a couple of years ago and if you look at some of the results from the weekend maybe the gap between the Premiership and the other leagues is not as big as people think.
"There have been a few shocks and I suppose our result will go down as a bit of a shock because people expected us to win.
"I thought Luton were excellent and you have to give them great credit. They played very well the last time we were down here and they raised their performance again this time.
"They deserve all the plaudits they will get from this, but hopefully now we can finish the job at home even though we realise it will be a tough game."