However, the Warwickshire allrounder was less effusive when it came to the future of head coach Chris Silverwood.
England suffered an innings and 14-run loss to Australia on Tuesday in Melbourne as Root's team surrendered the five-Test Ashes series with two tests to spare.
Root, who was reluctant to discuss the long-term future of his captaincy after the Ashes defeat in the third Test, has not won any of his three Ashes series in charge.
The 30-year-old, who will overtake predecessor Sir Alastair Cook's record of 59 Tests at the helm when he leads the side out in Sydney on January 5, has also suffered a record nine defeats in 2021 as captain.
Asked if the England players would support Root's continuation as skipper, Woakes said on Wednesday, "Absolutely. It's clear that the captaincy isn't having an effect on his batting, which a lot of the time with captains can be the case."
Root has proved a virtual lone hand with the bat and, after scoring 50 and 28 in Melbourne, he finishes the calendar year with 1,708 runs -- the third-highest after Mohammad Yousuf (1,788) and Viv Richards (1,710).
"The fact that he's scoring the runs he is, is great for the team," Woakes added. "It would be great if we could help him out with that and build some partnerships with him, and score a few more runs around him.
"But Joe is a great cricketer, he's got a great cricket brain. I think his record as England captain is pretty good, as far as I'm aware. I definitely feel like Joe will continue."
Asked if Silverwood, who is sole selector as well as head coach, also has the same support, Woakes added: "Who am I to talk about people's futures other than my own, to be brutally honest? We have two more games and we want to show a lot of character, a lot of fight.
"The group of players, the management and the staff we have out here have the backing of the players to hopefully put things right, over the next two games in particular."
Woakes was one of 10 England players to return to the MCG nets on what should have been day four of the Boxing Day Test, as work began on averting an Ashes whitewash.
The top three of Zak Crawley, Haseeb Hameed and Dawid Malan - who scored a combined 38 runs in the match - did come for a bat.
They were joined by the seven squad members who did not feature in the match for a workout led by Silverwood and assistant Graham Thorpe.
British media reported that the England board's chief executive Tom Harrison met Root in Melbourne on Wednesday to discuss the reasons behind the failing tour but the board is said to be supportive of him staying on as captain.
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