The tourists have lost the first three Tests of the five-match series, most recently tasting defeat by an innings and 41 runs at the WACA in Perth.
Despite surrendering the urn at the earliest possible opportunity, and the real prospect of a series whitewash Down Under, Harrison claims that the goal is still to become the best cricketing side in the world over time.
Speaking to Sky Sports News about the future of Trevor Bayliss, the ECB official said: "Trevor has done an excellent job. I don't think this is the moment for rash decisions. Ultimately, we have a plan and we're executing that plan.
"Winning away from home has been tough for this side for a couple of years, but we did win in South Africa two years ago. We continue to strive to be better overseas to enable us to get to a point where we can try to get to number one in the world."
The fourth Test at the Melbourne Cricket Ground gets underway on Boxing Day.