"It was a tight game but I think we deserved to get something from it," he said after losing 1-0 to Walsall.
"We didn't get it, which means the season carries on to next Saturday.
"We've got it all to do next week, but we're capable of doing it, I knew that for sure. So now we have to dig in and go again next week."
A draw at home to Boston on Saturday will save the Dragons from League Two relegation.
Boston kept their survival hopes alive on Saturday with an 83rd-minute Drewe Broughton equaliser against already relegated Torquay.
Carey added: "It looked at one stage on Saturday that things would go our way.
"The fans behind the goal, who were magnificent again, let us know what was going on elsewhere.
"But five minutes later it turned around because we conceded and the place went a little quite.
"We're certainly good enough to stay in this league, as we've shown. The players have been magnificent for us. In the last few weeks they've been heroic.
"The three wins after the Notts County home game have been terrific. We were dead and buried at one stage but the players and supporters have brought this thing back to life.
"We'll go into the game next week knowing that a draw will do us, but we'll go out to get the win."
BBC