Manager Stuart McCall admitted to being "gutted" after a late goal denied his Motherwell side a point against Celtic.
The Steelmen had led at Fir Park through Michael Higdon but Anthony Stokes levelled and Gary Hooper fired the visitors' winner.
"I don't think we deserved to lose the game," said McCall. "The lads were outstanding. We played some good stuff.
"There was some good stuff from both sides, total commitment. It wasn't just a kick and rush game."
The match was poised at 1-1 for a long period, during which time both sides pressed for a winner and Paddy McCourt's driving run led to Hooper's goal.
"We're not a team that can shut up shop and sit back, we like to have a go," McCall told BBC Scotland.
"One bit of magic by McCourt when he came on has won Celtic the game. We had a lot of tired legs at the end."
Motherwell ended with 10 men after Tim Clancy was sent off for kicking out at Hooper.
"Speaking to Tim, he's kicked him so it's fully deserving of a sending off," said McCall.
The result allowed Celtic to replace Motherwell in second place in the Scottish Premier League, with both sides on 26 points and McCall's men having an inferior goal difference.
"I've been sick over the last couple of weeks telling everyone we can't split the Old Firm, let's be realistic, but we can aim for as high as we can get," added McCall.
"We don't want to get beyond ourselves and think we're better than we are but we've got an aim in mind and we'll keep it to ourselves.
"We believe if we can keep the squad together and we keep improving then we can give it a real go this season."