After blitzing the home side for the first 40 minutes and racing into a 2-0 lead through Eoin Doyle and Ali Crawford, it seemed a matter of how many Bolton were going to score.
But a defensive error just before the break allowed Tom Pett to get his side back in the game and trigger a tense second half that could have gone either way.
Matt Gilks made one stunning save to deny Pett a second – but Wanderers also missed good chances, with keeper Jamie Cumming also denying Doyle a brace with a block at his near post.
“It was a good away performance,” Evatt said. “We have got a lot to learn and we got ourselves ahead of the game with two very good goals and then a minute of concentration before half time saves us 45 minutes of very hard work in the second half.
“We have to learn from that. We have to see halves out because we all know 2-0 is a susceptible scoreline. But the way we saw the game out, the way we fought, we created the better opportunities second half, we could have made things easy for ourselves.”
Wanderers played some of their best football of the season in the first half at the Lamex Stadium and had it not been for home keeper Cumming, could have stretched their lead further.
Evatt is encouraged by the progression he has seen as the Whites chalked up a third win on the spin for the first time in 12 months.
“That’s what I was brought in to provide, counter-attacking football with a good tempo, and we saw that at times today,” he said.
“Results breed confidence and the players are starting to implement the work we’re putting in on the training ground. We have now more or less got our strongest squad out there and there’s competition for places, so all of them know they have to be on their games.
“We were a completely new staff, new group of players and it was always going to take time regardless of what we said in the summer.
“Fortunately or unfortunately the name on our shirt makes us everyone’s cup final in this division so we have to play every game like a cup final. I think the way we started today was excellent, it was just that lapse on 44 minutes and it changes everything. It should have been dead and buried but in the second half we saw it out and also had some good counter attacks.”
Evatt believes his players are now starting to come to terms with the challenges of League Two after last season’s relegation.
“This football club has been used to losing games for too long and all of a sudden defeat almost becomes acceptable, but it isn’t acceptable,” he said.
“You have to do everything to win and perform every time you go out on the training ground or the pitch, it has to have that importance. I say to the players repeatedly, to be winners and champions, you have to act like winners and champions long before you start to win games consistently, and what I mean by that is that the standards in training, the standards, how we act, if we’re late, sweeping the changing rooms, little things like that all make a difference. You act like winners and now all of a sudden we are winning games more consistently.”