The home side stormed into a three-goal lead after just 10 minutes thanks to stand-in skipper Mikael Lustig, Nir Bitton and fellow midfielder Tom Rogic and kept going with in-form striker Leigh Griffiths notching a double before the interval.
Half-time substitute James Forrest scored eight minutes into the second-half before Griffiths completed his hat-trick with Celtic's seventh and - after Hamilton's second-half substitute Eamonn Brophy got goal on the break as a consolation - Callum McGregor made it eight right at the end.
Deila was confident it was the biggest margin of victory of his managerial career - "I think so, I can't remember better" - and was pleased with the way his players kept going for goals after the points were effectively secured so early on.
The Norwegian said: "It was a fantastic night, a very good performance, we scored a lot of goals and could have scored more so I am very pleased with the boys.
"We deserved eight and we could have had much more, we had so many more chances
You always want games like this and I am very pleased.
"It is always hard to keep up the tempo and intensity when you are 3-0 up after 10 minutes but we did that very well.
"We looked sharp
I seen it in training that we have looked better and better and today you could see what kind of tempo we can play at if we play at our best.
"We have kept in going since June 20 and since Christmas we had some weeks with training and rest and now you see more energy in the team."
Hamilton player/manager Martin Canning vowed to battle on after another abject display and result.
The New Douglas Park side have now gone eight games without a win and are above 11th-placed Kilmarnock on goal difference and the demoralising loss comes after the recent 4-1 William Hill Scottish Cup fourth-round defeat by Annan Athletic at Galabank.
Asked if he was confident that will get the chance to get Hamilton out of trouble, he said: "We need to wait to see what happens.
"As long as I am doing it, I will be fighting, and continue to do the best I can.
"Obviously it hurts, I am hurting more than anybody, I can assure you.
"I am gutted, when you lose goals in that manner and concede three goals in 10 minutes, you are giving yourself no chance.
"We didn't have enough leadership to pull us together when we needed it.
"It is so frustrating but what I have to keep thinking is that this performance and result against Celtic, as much as it hurts, our season won't be defined by it but we have to make sure we bounce back in Sunday."
Source : PA
Source: PA