Salzburg 3 Celtic 1
Brendan Rodgers was left to rue the loss of disappointing goals after 10-man Celtic surrendered an early lead to lose 3-1 to Salzburg in Austria.
French striker Odsonne Edouard put the visitors ahead in the Europa League Group B fixture at the Red Bull Arena after less than two minutes using his pace and power.
The Austrian champions, who reached the semi-finals of the tournament last season, dominated thereafter and two goals in six second-half minutes from Munas Dabbur and fellow attacker Takumi Minamino, both from cut-backs, turned the tie around.
Celtic winger James Forrest was then sent off by referee Sergey Boyko in the 72nd minute for denying skipper Andreas Ulmer an obvious goalscoring opportunity and Dabbur slotted home the consequent penalty.
Ulsterman Rodgers said: "I think that the best team won.
"I thought in the first half we started well and by the end of the half we had frustrated Salzburg, you could see that in their game and play, and we carried a threat when we broke out of our shape.
"So the first half I was reasonably pleased with, the second half we gave away disappointing goals, that was the frustration for us and then from that they gain confidence.
"And obviously when it gets to 3-1 it is a difficult game for us with 10 men.
"The positives from the first half; it was compact and tight and we gave them problems when we were positive going forward, didn't concede too much from a defensive perspective but yes, it was a disappointing result for us in the end."
While Salzburg top the group with six points from six, Celtic have three from their win over Rosenborg at Parkhead.
The Scottish champions now face a double-header against RB Leipzig, starting with a trip to Germany later this month.
Rodgers stressed that his side will have to work on ball retention in the subsequent group games.
The former Liverpool boss said: "It was a great start for us. Good pace and strength and then a wonderful finish. You could see the confidence in the team right from the beginning.
"You can see how Salzburg play, they are a very good side but we limited them in terms of clear chances.
"But at this level you have to be better with the ball and keep the ball and be able to play quicker with minimal touches, otherwise you don't get a rest in the game and that hurt us.
"But the guys gave everything, even when down to 10 men they were running, fighting, working and as I said, we were just beaten by the better team."
SALZBURG: Walke, Lainer, Ramalho, Pongracic, Ulmer, Samassekou, Haidara, Schlager, Wolf (Gulbrandsen 79), Dabbur (Yabo 85), Minamino (Junuzovic 71).
Subs not used: Stankovic, Van der Werff, Prevljak, Todorovic.
CELTIC: Gordon, Forrest, Lustig, Boyata, Hendry, Tierney, Ntcham, Mulumbu (Christie 78), McGregor, Griffiths (Sinclair 60), Edouard (Morgan 82).
Subs not used: Izaguirre, Simunovic, Gamboa, Bain.
Match rating: 7/10
Referee: Sergey Boyko (Ukraine)