The draw gave Newcastle their first Premier League point since February and halted a run of eight successive defeats which had dragged them from mid-table security into a relegation battle.
After a toothless 3-0 defeat by resurgent Leicester City last weekend Carver suggested his defender Mike Williamson had got himself sent off deliberately.
Derby County manager Steve McClaren reportedly rejected the chance to join the free-falling club for their final three games of the season and Carver held crisis talk with the board to discuss his future.
Having fallen behind to Victor Anichebe's goal on Saturday Newcastle found themselves temporarily in the relegation zone but Ayoze Perez's equaliser lifted them back to 17th place.
Newcastle are still in a precarious position, one place and two points above the drop, but Carver said the mental boost of halting their losing run would give his side renewed optimism.
"That could be huge," Carver, who was heartened by post- match applause from Newcastle's disgruntled fans, told reporters.
"It was important to stop the slide and that run of defeats.
"There has been a lot said in the last week after the Leicester game and rightly so, but there was a response from the players and definitely from the fans.
"One thing I would say is when you see a performance like that -- and hopefully it's not too late -- is that the players do care and they do want to stay in the Premier League.
"It was a great reaction from the fans and it affected the reaction of the players. They showed great character and determination to come back.
"From the first whistle to the last there was one team trying to win the game and one team trying to stay in the game and wait for a set play."
Newcastle face fellow strugglers Queens Park Rangers and mid-table West Ham United in their final two Premier League games.
(Reporting by Tom Hayward, editing by Ed Osmond)
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