After a difficult year, England's draw against West Indies in the first Test is a huge step forward.
In the past 15 Test matches, the side has only won one of them, and that was against Australia in the winter.
They showed promise over the last two days in Antigua, but were unable to win the game against the West Indies on Saturday.
We showed a lot of character, according to Root.
England suffered a collapse on the first day as they fell to 48-4, before Bairstow's 140 helped them post 311.
The tourists declared on 349-6 on the fifth day after centuries from Zak Crawley and Joe Root, before the hosts reached 147-4 at the close.
The director of cricket, Chris Silverwood, batting coach, and head coach all left their roles after England failed to pass 300 in the 10th and final Test.
"I'm really pleased with the way we played, especially give the position we were in after that first hour," said Root, who now has 24 Test centuries.
The guys stayed calm and showed great maturity to get us to a total, especially off the back of a difficult winter and a difficult year.
England only had an outside chance of victory on the final day, but took four of their eight allotted overs either side of tea to boost their hopes, before Nkrumah Bonner and Jason Holder dug in with a stand of 80 that lasted 35.5 overs.
The tourists were limited by the absence of a fast bowler.
The way the guys stuck at it, especially having one bowler down as well, showed a huge amount of character and it was a huge step forward in many respects.
No one stopped believing or giving up all day. We gave ourselves the best chance of victory.
Wood injured his ankle on the third day of the first Test and is a major doubt for the second.
England said Wood tried to bowl in the nets before the start of the fifth day but struggled with pain.
Uncapped duo Saqib Mahmood and Matthew Fisher are the other seam-bowling options in the squad, while Ollie Robinson missed the first Test because of a back injury.
James Anderson and Stuart Broad were left out of the England team for this series, but neither is on the list of reserves.
Mark will be assessed in Barbados and we will see how he is when we get there.
You know how much it hurts him, so it is bitterly disappointing for him. He is a wholehearted player and will never let anyone down.