The home side were shocked to lose a goal to Rapid striker Nikica Jelavic after only three minutes but recovered to level in the 20th minute through Scott McDonald.
Celtic find themselves bottom of Group C with one point after two games and face Hamburg at home later in the month and Tony Mowbray accused his side of shooting themselves in the foot at home once again.
“I think we did enough to get the three points over the 90 minutes,” he said.
“And yet, in the last three (home) games, we’ve shot ourselves in the foot. Within five minutes, we’ve lost a goal at home and had to go chasing the football match.
“That’s something we need to address very, very quickly, stop giving teams a goal start, particularly counter- attacking teams, who come and flood everybody behind the ball and try to hit you on the break. That said, I thought we stuck to our task well.”
Mowbray said of Stephen McManus’ mistake which led to Rapid’s opener: “Don’t play silly little balls into their midfield. The individuals who have made the mistakes have got to concentrate better.”
Mowbray believes he has seen enough in the games against Hapoel Tel Aviv and Rapid to be confident of beating them in the reverse fixtures.
He added: “Hamburg is a big test for us. Back-to-back games now and they are big games for us.”
Goalscorer McDonald said: “We’re disappointed not to get three points in the end. After the goal, we looked in control but we just couldn’t put the ball in the back of the net.
“We put it in once but not twice.”
CELTIC: Boruc, Wilson, Caldwell, McManus, Daniel Fox, McGeady (McGinn 81), Brown, N’Guemo (Robson 81), Maloney (Killen 81), McDonald, Samaras.
RAPID VIENNA: Payer, Dober, Patocka, Soma, Katzer, Heikkinen, Pehlivan, Kavlak, Hoffmann, Boskovic (Drazan 63), Jelavic.
Referee: Bruno Miguel Duarte Paixao (Portugal).