Maxi Rodriguez scored the only goal of the game in the 86th minute.
“I don’t think anyone deserved to win to be honest,” Carragher told Sky Sports.
“I don’t think there were too many chances. It’s always a difficult game here at Bolton.
“Kevin Davies had a header late on, and that could have been it for them, and our chance has gone in.
“It was a really tight game but that’s the Premiership for you.”
The win moved the Reds out of the bottom three of the Premier League.
He added: “It’s just nice to be out of the bottom three. We’ve been in there a while so it’s been difficult to look at the table.
“In the weeks to come we have to get further up the table.
“We know we haven’t had a great start, but there’s still a long way to go and with the league so tight, with a few wins we can certainly climb to the top half of the table.”
