Latics dominated the game in terms of possession and chances, and could easily have doubled the winning margin such was their superiority.
Marc-Antoine Fortune grabbed the opening goal after just five minutes, with an own goal from Elliott Ward and a wonder goal from Jordi Gomez completing the scoring after the break.
"We started the game very well - the scoreline at the end could have been the score after 20 minutes," Barrow said.
"In fairness to Bournemouth I thought they came into the game a bit before half-time and asked some questions.
"We sorted ourselves out at half-time, and I thought we were quite convincing in that second half.
"We've set some standards now and we've got to keep that going.
"We've had quite a few players out injured but we keep churning out performances and it's going okay."
The win extended Wigan's unbeaten domestic record under Rosler to seven matches.
But Barrow says no-one at the DW will be getting carried away just yet.
"I personally think there is more to come from us, which is a very positive sign," he said.
"We're not getting carried away, especially not under the gaffer - because he won't allow us to do that.
"He's very similar to Roberto Martinez in terms of work ethic, and I think everyone at the club appreciates that.
"The proof of the pudding is in the eating, and we are improving.
"But we know we have to carry on improving, and no-one here is getting carried away."
- Sports & Recreation
- Elliott Ward