The Potters' dug in deep and clawed a crucial victory against the Merseyside club after Carragher gave away a decisive penalty.
Speaking to Sky Sports News, the Englishman admitted: "That's the Premier League and that's football, it's Stoke's day today.
"We can probably be pleased with the way we've performed but at the end of the day we've come away with nothing.
"They defended great. They do great, their keeper and the back four. They've been like that for a long time, especially at home.
"And, being a defender myself, you can only admire how they did it, especially in the second half."
Carragher was also hesitant to comment on the penalty he conceded, saying: "I'd like to see it again but at the time I thought it was a little bit harsh. It may have been or it may not have been, I'll have to have a look at it.
"One has gone against us and the others haven't gone for us, so we feel a little bit aggrieved.
"It's a disappointing day but if we can play like that at Spurs hopefully we'll get something."