The hosts ran out of time in their bid to bowl out Australia and level the series but Root insists the performance improved the mood ahead of the third Test at Headingley.
Root said: “I think it was important that we bounced back strongly after Edgbaston and I think we’ve certainly done that.
“We’ve proved that we’re still in this series and we will take that momentum going into the next game.”
Root said he had no regrets about the manner in which his team came up short after their chances were drastically reduced by the earlier rain.
Australia hung on at 154 for six after Ben Stokes’ century had allowed England to declare with a 266-run lead.
“It could have made a big difference but you can’t control the weather,” added Root.
“We had to get ourselves to a score where we thought we were in control of the game and we managed to do that.
“Ben (Stokes) played exceptionally well and then we threw everything we could at them, and fair play to Australia, they managed to hold on.”
Stokes, who made an unbeaten 115, added: “It was nice to get a hundred. We fought incredibly hard there towards the end. Fair play to Australia for holding out.”
Australia captain Tim Paine was full of praise for Steve Smith’s concussion replacement Marnus Labuschagne, who came in to score a crucial 59.
“It was really pleasing for us to see him do that. To be able to stand up and play the way he did for such a young player was fantastic,” Paine said.
“We’re here to win the Ashes and I think we were probably a fair way off our best in this match.
“But part of becoming a good team is finding a way to get draws out of days like today.”