The former European champions are unbeaten since Barlow, a former Scunthorpe manager, took charge alongside Ian McParland.
Forest have won their last six games to rise up to sixth in the table, the final play-off position.
But Barlow has warned that the momentum must continue in their final three games of the season, including Saturday's tricky trip to relegation-threatened Hartlepool
He said: "We can't afford to stutter. We couldn't afford a hiccup when we were trying to get into the play-offs, and nothing has changed now."