Former Celtic striker John Hartson suggested the side looked nervous in their 1-0 Champions League qualifying win over KR Reykjavik.
However, the Welshman expects Celtic to improve under new manager Ronny Deila as they aim for the group stage.
Callum McGregor scored on his first start for the club six minutes from time to give the Norwegian a debut win.
"I think he would have been nervous, the players were anxious to impress," Hartson told BBC Radio Scotland.
"It's his first game, his first competitive match in charge.
"He's got a new coaching line-up alongside him, he had John Collins last night, so everyone will be nervous, everybody will be anxious.
"Everybody wants to have a look at Ronny Deila - the way he sets up, the way he wants to play, what are his tactics are going to be like, what's his philosophy. Does he want to play through the middle, does he want to kick it long?
"I think the Celtic fans will give Ronny Deila a fair crack of the whip. They'll back him but at Celtic you have to win and he's got off to a winning start."
The Scottish champions dominated but repeatedly failed to find the breakthrough before 21-year-old McGregor's deflected shot gave them the advantage ahead of next week's second leg at Edinburgh's Murrayfield stadium.
"I thought it was pretty comfortable to be honest for Celtic," said Hartson. "I know they only scored in the last 20 minutes, but I just felt over the 90 minutes Celtic could have won four or five-nil.
"Kris Commons hit the crossbar, [Leigh] Griffiths hit the crossbar. Commons was wasteful with one or two opportunities.
"I didn't see a lot in the opposition to really mount any sort of challenge, so I thought it was a good performance and Ronny Deila has a lot of positives to take from it.
"McGregor looks good out on that left-hand side and I thought the shape was excellent.
"Although 1-0 looks as if it was a difficult night, it really wasn't. I thought Celtic totally dominated and I didn't think Reykjavik had the quality throughout their side, so I would call it that Celtic will go through reasonably comfortably when they play at Murrayfield.
"In terms of upping their game, I think they will naturally, as that was their first competitive match last night and it's always difficult in your first game.
"Celtic will need to improve, but I think they will as the weeks go on and all the Celtic people out there will hope they can get Champions League football again this year."