The Bantams hosted their South Yorkshire rivals at Valley Parade on Friday as the visitors claimed a 4-3 win in Bradford's second private friendly ahead of the 2020-21 campaign.
Clarke scored one of the Bantams' goals while Kurtis Guthrie completed the scoring for the home side.
City begin their campaign with a League Cup tie at Bolton on September 5 before opening their League Two season with a home fixture against Colchester United a week later.
“It was a good exercise for us, to get minutes in the tank. It was also great to be back out on the Valley Parade turf," said Clarke of Friday's outing, which was Bradford's first on home soil since February.
“We scored some really good goals and, overall, it was a productive day. There were plenty of positives to take from the performance.
“Although we are still only in pre-season, we want to enjoy good form and carry that into the campaign. We have had a long lay-off and to be back playing games and improving is key, at this stage.
“Getting on the pitch and contesting matches is where you learn the most. Coming up against a good Doncaster side was an important test.”
Clarke is in his third spell with the Bantams, joining the club on a one-year deal last month after leaving Grimsby Town.
The seasoned campaigner has been encouraged by what he has seen during pre-season training, as City look to mount a promotion challenge.
“There have certainly been encouraging signs in training and we will keep the effort levels high," added Clarke.
“We need to be fit and sharp all over the pitch, to be able to play the way we want to, over the course of the season.
“Some teams will come and try to play out and really take the game to us, and others will not. It will vary on a game-by-game basis, but we have the adaptability to play in different ways.
“With the group of players we have, high energy off the ball is key, and when we are on the ball, we have players who will make things happen.”
Bradford face Huddersfield Town in a friendly at the Terriers' training base on Wednesday, in another meeting which will be strictly behind closed doors.
Meanwhile, Doncaster's campaign gets underway in just seven days as they face Blackburn Rovers in the League Cup on August 29.
Support The Yorkshire Post and become a subscriber today.
Your subscription will help us to continue to bring quality news to the people of Yorkshire. In return, you’ll see fewer ads on site, get free access to our app and receive exclusive members-only offers.
So, please - if you can - pay for our work. Just £5 per month is the starting point. If you think that which we are trying to achieve is worth more, you can pay us what you think we are worth. By doing so, you will be investing in something that is becoming increasingly rare. Independent journalism that cares less about right and left and more about right and wrong. Journalism you can trust.