Ronaldo, 36, returned to Manchester United of the Premier League this summer after the club agreed with Juventus on his transfer, and marked his second debut with the team against Newcastle United in early September.
Carragher, who is known to not be fond of Ronaldo’s arrival, told The Telegraph that they remained "a team of individuals rather than a team."
“Cristiano Ronaldo has added to that rather than fixed it."
Carragher referred to the team as a “brilliant squad,” which was not yet at the level of the other three teams. “Dropping five points in their last two home games highlighted lingering inconsistency," he remarked.
Ole Gunnar Solskjaer’s team have now dropped five points in their last two home games and won one in four at Old Trafford in all competitions.
The team's recurring failures prompted Portuguese footballer Bruno Fernandes to raise his own concerns after the 1-1 draw against Everton.
“These last two games at home [were] not good enough in the Premier League,” the midfielder said. "If we want silverware at the end of the season, we have to do much better.”
Carragher added that champion Manchester City remain the team to beat in the Premier League after the opening seven games of the season. “They have gone to the two toughest venues and taken four points, justifying being favourites to win it again. They will take some stopping.”
Ronaldo recently sent a message out to his fans through an Instagram post in reaction to the loss against Aston Villa last week, reminding them that great things were on the horizon as the team would be fighting in the ranks.
“This is only the beginning, but in a competition as strong as the Premier League, every point counts! We must react immediately, get back on our feet and show our true strength,” he said.
Man U's next chance at claiming points comes on Saturday, when the team faces off against Leicester City.