The centre-half looked to have put United in a difficult situation less than a minute into the contest when he bundled over Umut Bulut inside the area. However, despite vociferous appeals from the Turkish outfit, referee Wolfgang Stark refused to point to the spot.
Still, despite being cleared of any wrongdoing during the match Vidic was quick to admit that he believed he had indeed fouled the Galatasaray striker.
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"We scored a goal at the right moment, but then I believe we were nervous for 10-15 minutes. In the second half, we were stronger.
"The first game in the Champions League is always hard. We started well, but after that we made a few mistakes and caused ourselves some problems. It was tense in the end, we defended a bit more than we wanted but the main thing is we won the three points."
Michael Carrick's seventh minute strike gave United the lead, and they missed a golden chance to seal the points when Nani's spot-kick was easily saved by Fernando Muslera after Rafael had been brought down inside the box.
That miss was Sir Alex Ferguson's side's third of the season after Javier Hernandez had also been denied from 12 yards in Saturday's 4-0 over Wigan and Robin van Persie fluffed his effort against Southampton, and Vidic feels that the Red Devils need to work on their spot kicks if they are to improve in that area.
He added: "I missed one as well for the national team! I think we've had many players who've missed penalties over the last six months, obviously it's something we should work on."