It was the fourth win in a row for Celtic, albeit the William Hill Scottish Cup final victory over Hearts at Hampden Park on Sunday required a penalty shoot-out.

The champions remain 16 points behind Rangers, who won 3-0 at St Johnstone, with three games in hand and the Hoops boss was happy to see continuing improvement.

Lennon said: "We should have won the game by more.

"It was a clean sheet and we didn't look in any trouble. We seem to be going in the right direction again.

"We missed some great chances and the quality of what we created was high.

"I am delighted, though. It was a good performance. Overall I am really pleased and it's a step in the right direction.

"We got a lift from the weekend win and that pressure and anxiety has gone now.

"We are looking forward to the league games now and it's good to get a win to start the Christmas period.

"There is a feel-good factor. We just want to keep the squad bubbling over now.

"We are still a long way back and we won't get too high or too low. It's a game at a time but we are taking steps in the right direction."

County have now lost five games in a row – four in the league – and remain four points behind second-bottom Hamilton at the halfway point in the season but Hughes was encouraged by what he witnessed.

The former Hibernian and Inverness boss, who took over from Stuart Kettlewell on Monday, said: "I was quite glad we were coming to Parkhead because we were playing against the champions and I could see who was up for it, I could see what we have got and see who was fazed by it.

"In terms of quality, I am honest enough to say it has to be better, ball retention has to be better.

"In terms of effort and commitment, it was very good.

"The goals we lost were preventable and we have to stop that but in terms of togetherness, I saw that tonight.

"There is enough there for me to know that if we get a wee bit of luck we could be alright."