Carson, 35, made his City debut in the 4-3 win over Newcastle, even saving a penalty that was eventually bundled home by Joe Willock.
His last Premier League game came 10 years ago - ironically away to Newcastle in a 3-3 draw with West Brom.
"The people maybe don’t know, but he’s a real leader.," said Pep.
"He says what he believes, he’s got a lot of experience with big teams.
"He’s an incredible person and we are delighted - Eddie and the players too - that he could play.
"He couldn’t do anything for the goals but I am so happy he could make a debut for us."
Watch Pep's full press conference on the video above.