Two late goals from striker Jamie Proctor ended a run of four successive draws for Barker's men as the Alex went down to their first defeat in four games.
Barker said: "This keeps us in contention, and puts us right back in the race again. It was the only game and someone had to make ground, whereas the team that lost effectively dropped out of the play-off contest."
Crawley are nine points adrift of a top-six spot and Barker is keen to continue the momentum going into Good Friday's home game against Stevenage.
He added: "We've three games in six days and hopefully we can carry on the momentum. We are on course for the time being but a lot will be decided over the next six or seven days.
"The league table will look very different on Monday evening. We are on a good run of form and it is a fantastic opportunity for us. The players are enjoying themselves and we must be one of the most entertaining teams to watch in the division."
Crewe manager Steve Davis admitted his side only have a "very outside chance" of forcing their way into the play-offs with nine games remaining.
He said: "It does us no favours. We needed to win this game but for both teams it will be a tall order. Crawley are only two points ahead of us."
The match was quickly re-scheduled after last Saturday's postponement and Davis said the preparations were not ideal.
He added: "We had a long wait for this game. At the end of the game we looked tired and leggy."