Derek McInnes felt losing to Celtic by two goals was "harsh" on his Aberdeen players but accepted the first-half award of a penalty was justified.
Goalkeeper Jamie Langfield was sent off after felling Georgios Samaras and Kris Commons netted from the spot.
And James Forrest's late cross deflected past substitute keeper Nicky Weaver to double the visitors' lead.
"Plenty of endeavour, big hearts from the players," McInnes told BBC Radio Scotland. "We'll pick ourselves up."
The Dons went into the match off the back of two straight Scottish Premiership wins and McInnes was pleased with how the hosts competed before and after being reduced to 10 men.
"I think 2-0 is harsh on us," he explained.
"The decision to give the penalty was absolutely right. Jamie has caught Samaras. I'm disappointed we allowed that situation to arise in the first place.
"We just had to make sure we stayed in the game.
"I thought we had a good temperament for it. I thought we had enough belief. I'm delighted with how they kept going.
"It was a big, big effort from everybody. We've got good players.
"We've got to make sure we kick on. We've got a lot to look forward to. We've got work to do."