After getting a deserved opening-day point against Dundee United, Killie followed a 2-0 Ibrox defeat with a 5-0 thrashing at the hands of Celtic on Sunday.
“The manager said to us in the changing room afterwards that the season starts now," Donnelly said.
“It’s still difficult to take the Celtic result with the way we conceded the goals, but it is the Old Firm and the games coming up are certainly a lot more winnable.
“We conceded a few shoddy goals which doesn’t help things and we have to try and cut them out of our game.
"We’ve had two weeks which have been as much about keeping the opposition out as thinking about our own game.
“But the next fixtures should be a bit more of a chance for us to impose our own style onto matches and play some of our own game.
“With that in mind, we have to try and get a few results.
“Of course, we are going to be hurting with Sunday's result and it is going to be frustrating for the fans to watch at times as well.
“But, look, confidence is not dented. We have a big game against Ross County on Saturday and that’s the beginning of a run of fixtures where, hopefully, we will be able to get a few wins.
“But we won’t take anything for granted as we know that every game in this league is a difficult one and that begins with Ros County."
The games have also been valuable exercises for Donnelly after he missed the start of pre-season before signing for the club following his exit from Motherwell.
The Northern Ireland international said: “It gets you up to speed, yes. But it is obviously also difficult to play in them as well in terms of fitness.
“I missed a bit of the pre-season so getting a little bit of fitness back in from playing in a game like that certainly helps."