McClaren was backed with funds in the January transfer window, with the Magpies spending more money than any other team in England.
And Redknapp believes that Newcastle have now assembled an impressive squad, which should have enough quality to keep them in the top flight.
“It was a good transfer window for Newcastle,” Redknapp said. “If it proves to be the difference between relegation and survival then the fans might have to give Mike Ashley a bit of credit.
“It’s not been a good season on Tyneside but that was a huge win against West Brom. Lose that and the pressure would have been immense.
“But now they have some decent attacking options with Georginio Wijnaldum, Moussa Sissoko, Andros Townsend and Aleksandar Mitrovic, while Jonjo Shelvey is pulling the strings in midfield.
“Given how much money they have spent, Steve McClaren really won’t have any excuses if his side don’t stay up now.”
Newcastle’s 1-0 win over West Brom last weekend has finally taken them out of the relegation zone.
McClaren’s men have been stuck in the bottom three for much of the season so far, but they have now leapfrogged Norwich City into 17th place in the standings.
Newcastle’s new signings also seem to have settled in well, with Jonjo Shelvey and Andros Townsend both catching the eye against the Baggies.
Newcastle’s next fixture comes against Chelsea at Stamford Bridge, and if they are able to cause an upset against Guus Hiddink’s improving side, they could put even more distance between themselves and the danger zone.