Carver's men suffered a 1-0 loss at the Stadium of Light last weekend thanks to Jermain Defoe's superb strike, marking Newcastle's fifth derby reverse in a row.
Newcastle visit Liverpool in the Premier League on Monday and Carver has urged his players to put the disappointment behind them.
"Monday was one of the darkest days of my career and I'm still hurting," he said. "I have to try to not show it in front of the players.
"We have seven games now and it's a seven-game season. The next couple are tough but after that they look a bit more favourable.
"Liverpool are only seven points off the top four with seven games to go. Anything is possible and they will believe they can do it."
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