Late goals from Wayne Rooney and Javier Hernandez secured a 3-2 victory for United against Stoke - who twice led at Old Trafford.
The result eased some pressure on United boss David Moyes following a stuttering start to the campaign, and Carrick concedes the team has to go on a winning run to lift morale among some of the club's fans.
"We've been saying for a number of weeks when we've had a good result we have to kick on and get back to our normal selves," Carrick said.
"We've still got a way to go, we're not kidding ourselves. We've had a couple of good results but by no means are we at our best - we're not in bad shape but there's more to come.
"There's no point looking at the table at the moment. Obviously we're aware of the situation but there's no point going over it in your head thinking 'what if', we've just got to concentrate on getting the wins and see where that takes us."
But the 32-year-old reckons the signs are good for United who demonstrated a familiar trait with their late winner on Saturday.
Carrick added: "It's the character we have - it was a vital game to win. We didn't really have a choice, we had to find a way and we kept going and believing and ended up finding that win."