But a fortuitious effort from City captain Gary Jones reduced the deficit soon after the interval before James Hanson ensured the contest finished honours-even.
"The only thing that I'm disappointed with is the result," Clough said. "I can't be disappointed with the performance.
"What changed that was the deflected goal. If it hadn't been for that then I think we'd have gone on to win. Without a shadow of a doubt.
"That gave them (City) something to hold on to and cling on to.
"I don't actually remember our keeper having a great deal to do. Credit to Bradford because they showed lots of character.
"But so did my lads. They have given everything out there, absolutely everything.
"What they didn't get, however, was that lucky break."
Clough added: "That was everything you'd expected from a derby.
"There was passion and commitment aplenty.
"If we carry on showing the same levels of that then we'll be ok, I'm convinced about that."
United landed the first blow of a pulsating first half when Murphy claimed his fourth of the season after just eight minutes.
Tony McMahon, finding himself in time and space on the right flank, drove an angled centre across the visitors' penalty box for theformer Motherwell winger, ghosting beyond Stephen Darby, to prod home from close range.
Maguire doubled United's lead just before half-time. Baxter, who later flashed wide from long distance, whipped a corner towards the far post and the centre-half claimed his sixth of the campaign after beating Jones and Jon McLaughlin to head home.
City equalised when Jones' deflected shot completely wrong-footed George Long before the United goalkeeper diverted the City captain's free-kick into Hanson's path as City restored parity.
Stephen McGinn drew a fine reaction save from McLaughlin after being released by Tony McMahon, Maguire glanced wide and Jamie Murphy went close as United pressed.