Newcastle United have taken eight points from their last four matches.
Taylor and Shelvey were both handed important roles during Benitez’s initial time at the helm, but after a 3-1 defeat to Southampton they dropped out of favour.
Newcastle have since gone on to take eight points from their last four matches, as they have moved out of the Premier League’s relegation zone.
And Carragher believes that Benitez’s decision to drop both Taylor and Shelvey has been crucial in the Tynesiders’ improvement.
"I think (the revival) started four games ago and I think it started in the Southampton game," Carragher said. "Enough was enough – and the shambolic first half when they were two down. They went on to lose 3-1 and the two fall guys have been Steven Taylor and Jonjo Shelvey, the £12million signing – he may even have been captain on the day.
"Rafa Benitez would not want to see teams coming through the centre and passing his midfielders. I know he sets his teams up well.
"He came to the game at home to Swansea and it was win-or-bust. The team that he played then, 10 of the 11 have played the last four games for Newcastle but when the team came through for that Swansea game, there were a lot of raised eyebrows from Newcastle fans.
"I think the fact that Sissoko had been given the captain’s armband in that number 10 role and Cisse was playing instead of Mitrovic (was a surprise). Tiote was playing as well and let’s not forget they are two players that nearly left in January. Jamaal Lascelles was starting as well and I think he’s been absolutely outstanding in that role."
In Taylor’s absence, Lascelles has stepped up and formed a good partnership alongside Chancel Mbemba at the heart of Newcastle’s defence.
The Magpies have conceded just three goals in their last four matches, with the strength of their defence giving them a solid platform to build upon.
Part of the reason for this has also been due to the increased protection that they have been offered by their midfield.
Cheick Tiote has been selected to play alongside Jack Colback in the heart of Newcastle’s midfield, and the pair have been very difficult for opposition sides to break through.
Newcastle’s remaining fixtures this season come against Aston Villa and Tottenham Hotspur.