The Scottish champions triumphed 2-0 thanks to goals from Jan Vennegoor of Hesselink and Scott McDonald in a one-sided contest at Parkhead on Saturday.
However, both teams meet again immediately after the split and Calderwood has promised a vastly improved performance from his players when Celtic travel to Pittodrie.
"It was always going to be very exciting," he said of the post-split fixtures.
"Now we've got a chance to show Celtic what we are really worth in two weeks' time because that [the game on Saturday] wasn't good.
"It could be a good thing for us but we will just have to wait and see.
"We would expect a reaction against Celtic."
Calderwood has also refused to give up hope of securing the coveted third spot behind the Old Firm, which is currently occupied by Hearts.
"We've got three games at home after the split and we expected that," he said.
"If we want any chance of finishing third, we've got to win four out of the five games.
"If we want to finish fourth - if that's the only option for us - then we've probably got to win at Tannadice and win another two games."
The Dons hosted Rangers when the Ibrox side's championship bid ended on the final day last season.
And, despite managing to avoid the Old Firm in the final round of fixtures this time around, Calderwood refused to rule out having a say in the destination of the title once again.
He told RedTV: "I've been involved in most of them on the last day so it's a nice change.
"But you never know. We're at Ibrox in the second-last game and, if we win there, we could decide that the championship goes to Celtic Park.
"We'll just have to wait and see but it's not the last game of the season which makes a pleasant change."
Meanwhile, Calderwood has written off any chance of Celtic and Rangers being included in a proposed Premier League II.
He said: "I would be amazed if it happened - absolutely amazed.
"I don't think it will happen because I've spoken to too many down south who don't want it to happen."