The hosts, who drew 1-1 in Istanbul the previous week, were level going into the final 30 minutes but the visitors’ ultimately became too much in the end.
Considering the gulf in size and resources of the two clubs, it was a spirited effort from Callum Davidson’s side, who will now drop into the play-off round of the Europa Conference League where they’ll meet LASK.
The Austrians reached the quarter-finals of the Europa League in 2019-20 and defeated Sporting Lisbon to qualify for last year’s group stages.
However, Booth insists the St Johnstone players will take plenty of heart from the display over their last two European outings.
He said: “It was an incredible performance over the two legs, to run a team like that so close. We were right in it for a game and a half, which is an incredible effort when you look at how much quality they have.
“I think I saw their wage bill is more than fifty times ours. They have players like Falcao who wasn’t even in the squad, some incredible talent. But we went toe-to-toe with them for a long time and proved how good a team we are.
“It was disappointing to go out of the Europa League but as the manager said in the dressing-room afterwards, we have a lot to be proud about and we have to use that next week now.”
One player who certainly looked at home against such fearsome opposition was young midfielder Ali McCann, who sparkled in the centre of the park.
“Ali was unbelievable over the two legs,” Booth continued.
“Everyone in Perth knows what a good player he is and against Galatasaray he’s taken that to another level. He has been our best player in both games.
“He’s the best young player I’ve played with. When I first came in, after about a month I thought that and he’s only proved it since.
“He’s only 21 still and he’s got everything in his game. He’s only going to get better as well.”