Teenage striker Charlie Ide grabbed a point for the Bees by levelling the score at 2-2 two minutes into second-half stoppage time.
And Fitzgerald, who replaced Leroy Rosenior earlier in the season, believes his side are now on the right track.
"We kept going right to the end and got the reward," said Fitzgerald.
"Anyone who doesn't do that won't be in my team, we have to use this result to kickstart our season."