The 0-0 draw handed Gers an immediate £10 million pay-day. Smith felt McGregor's first-minute save from Igor Burzanovic, after Carlos Cuellar misjudged a long ball over the Rangers defence, set the tone for the rest of the game as the visitors secured the goalless draw which took them through 1-0 on aggregate.
McGregor went on to make several more crucial saves to keep Rangers on level terms, including a stunning tip-over from Ognjen Koroman's fierce 25-yard drive in the second half.
"We expected furious attacks from Red Star at the start of the game, and I must say that our goalkeeper really did great when he saved Burzanovic's shot," said Smith.
"It was a one-on-one situation, when you can only hope your goalkeeper will be better then his rival. And Allan McGregor really reacted bravely, and saved the team in that first minute.
"After that, he was in the right place, calm and ready for two or three chances, but we've had our own too, such as our penalty claim after Jean-Claude Darcheville went down in the area.
"This is a huge success for everyone at the club. To be in the Champions League is something we've wanted, and something that was our major goal at the start of the season.
"The atmosphere at the stadium was really at the highest possible level, but my players withstood it well, and used it to their advantage, not disadvantage.
"It's not easy to play such an important game in front of a crowd, but my whole team used that to raise the quality of their own performance.
"The guys kept their nerve, they stayed fully concentrated and I must congratulate them for their effort.
"I must say that this is a really great result for the club, as we've faced a crucial match without knowing how our new signings would handle this kind of hostile environment.
"And they stood up to it. That is something that make me really proud.
"But I'm proud of other things. We finished these qualifiers without conceding a goal, and we've had seven Scots in our starting line-up.
"That fact is maybe the biggest bonus, along with our qualifying for the group stages of the Champions League."
Red Star manager Milorad Kosanovic told the after-match press conference that the best team had been eliminated.
Kosanovic said: "We were unlucky not to go into the group stage of the Champions League, as we've shown in these two matches that we are better than Rangers.
"But when you miss chances like we did today in the first half, and when your only mistake, in the 90th minute of the first leg, costs you a goal, then you have to accept that you are out.
"In modern football, at this level, details decide matches.
"Rangers used their enormous experience to stop our forwards.
"They were on the brink of conceding a goal at some stages, but they stayed calm and prevented us cutting that deficit from the first game.
"Still, I think my team gave their best in both games, maybe even played better then they can usually, but that wasn't enough to go through."