Rangers and Celtic both crashed out of the tournament before the draw for the quarter-finals took place at Hampden on Thursday.
But rather than be concerned by the lack of Old Firm interest, Doncaster insists there are plenty of "tasty ties" left in the competition to motivate fans to come out in their numbers.
He said: "We are very hopeful, with the draw being as wide open as it is now, it will enhance the spectacle and entice more people to come along.
"It's the first piece of silverware that will be won across the whole league this year and I'm sure the eight teams involved will all fancy their chances of putting their hands on the trophy."
Rangers exited at the first hurdle to Forfar, while Celtic suffered a shock defeat to Morton midweek.
Doncaster added: "One thing about running a cup competition is that you can't predict what's going to happen.
"The club's still involved must all feel that they've got a real chance of making their way to the final.
"I'm sure they will be looking forward to the ties coming up."
As well as a last-eight Edinburgh derby between Hibernian and Hearts, Dundee United will travel to Inverness, Morton will host St Johnstone and Aberdeen make the trip to Motherwell.
Doncaster said: "With seven Premiership clubs in the draw, but without Celtic and Rangers in there, I think it's wide open.
"I wouldn't want to be a bookie predicting who's going to do well in this competition now. Clearly there are some very tasty ties in there.
"I was at the Falkirk v Aberdeen game and it certainly seemed relevant to the Aberdeen players who put in a scintillating performance.
"I think it does mean a lot to the players and the managers involved and they will want to make their way to a final and hopefully earn a piece of silverware."
The League Cup - as well as the SPFL as a whole - is still without a sponsor.
Doncaster said: "It's a big national cup competition and we believe we've got a lot to offer.
"What's important is that we take our time to partner with the right sort of organisation, who we feel is a good fit for the SPFL."