Despite being ranked fourth in the world, England have won just three of their six World Cup matches this campaign.
Two of them came against San Marino — the worst team in the world — with the other coming in Moldova.
Carrick said: “We believe in ourselves, we believe we’ve got a good chance to go through.
“We’ve got four games to go — four huge games — but it’s hard to say how many points we’ll need. It depends on other results.
“I’m not thinking about not qualifying. We’re still in it, we’re in a good position.
“It is not ideal because we want to be top. But it’s up to us to get the results to make it happen.
“It’s still in our hands and if we win all our games... but it’s too easy to say that because there are tough games in the group.
“We’ve still got to go to Ukraine, so we can’t take anything for granted just yet.
“The game in Montenegro was similar to the Poland game, where we got ahead and found ourselves defending for longer spells than we should do, really.
“We are not out of it, it’s not a bad point.”