The Parkhead side were stunned when striker Lee Casciaro, who had scored Gibraltar's first international goal against Scotland at Hampden in 2015, sensationally put the part-timers ahead in the 47th minute.
Hoops striker Leigh Griffiths hit woodwork twice as the visitors battled back but the home side held out for a result which ranks as the most embarrassing in Celtic's European history, although the Scottish champions will fancy their chances in the return game in Glasgow next week.
Asked if there were red faces in the dressing room, the former Liverpool boss, who took over from Ronny Deila in May, said: "No
There is obvious disappointment
"There is no embarrassment
It was a tough game in tough conditions
We didn't take our chances, they took their chance.
"We dominated and created enough chances to score
Sometimes it can happen, obviously with the pitch, an awkward bounce and all of a sudden the player is in, it's into the floor and goes in.
"We have seen enough to see that we can get through in the second leg
Of course you are disappointed to lose.
"It was difficult, of course
They set up 5-4-1
And it doesn't matter the team, the level
Teams have good organisation, 11 players behind the ball.
"Throw the pitch into that, it's very, very tough for the players.
"But we created enough chances, their keeper made fantastic saves
It gives us a bit of work to do in the second leg."
Rodgers' message to Celtic fans, over 300 of whom were in the tiny stadium which was not full to its 2,000 capacity, was to "stay calm".
He said: "Celtic fans expect us to get through into the group stages
It was disappointing but the players gave everything they had.
"The message to them (fans) is to stay calm
This is a good group of players, they are working hard and in a week's time we will need them.
"I always thought this qualification phase would be based on the second leg at home, so we will need that support and hopefully get the job done next week.
"They were never in command
We were the team with dominance
What we lacked was the final touch, the final ball.
"I'm not really (shocked)
I've been around the game often enough, I know these results can happen
We stay calm
We need to put in a performance next week,
"The result here complicates it a bit for us
We move on to next week."
Lincoln Red Imps captain Roy Chipolina stood behind his comments earlier in the week when he said victory over Celtic would be the biggest shock in European football.
He said: "I think so
When you look at the history of both clubs
Nothing has changed, Celtic are still a massive club and they are still favourites in the tie, but I don't think anyone expected us to be going over to Glasgow with a 1-0 lead.
"We will be going over there more confident than we thought, trying to put the same shift again and, if miracles can happen again, we will knock Celtic out of the Champions League.
"It's just crazy and even when we go over for the second leg I don't think the lads will even believe that we have actually beaten Celtic
It is just unbelievable.
"Tactically we did exactly as the gaffer said
We knew Celtic would have most of the possession and the plan was to frustrate them and the longer the game went on the more frustrated they would become and hopefully open up at the back.
"We knew that if we got the chance, with Lee up front, he would put it away and that's exactly what he did.
"But we don't want to get carried away
We know Celtic will be up for the game when we go over, we are going to have to put in 10 times the shift that we put in here if we are to go through
Let's hope we do it."
Source : PA
Source: PA