Milan striker Filippo Inzaghi made history with his 63rd goal in UEFA club competitions - but could not stop Celtic joining the Rossoneri in the second round, courtesy of Benfica's 2-1 win in Ukraine.
"It was a tough group. I think after first two games you would have thought Shakhtar were favourites to go through. Milan are a fantastic club. We will now go to the hotel and enjoy it.
"I thought the game was dead because the game in the first half was dead and it came a little bit to life after the goal. It was a bit like the atmosphere, it was dead and it's difficult for the players and for the coach to deal with that.
"I was okay until Milan scored, then I got worried but I eventually got some thumbs up from several people and I knew everything was okay."
Strachan admits, however, his side must improve their abysmal away form.
"I think the next level for us is to be a force away in Europe. I need to find that out and do something about that," he said.
"We have to get better whether it's at home or away. There's one or two negatives I'm desperate to sort out."
Asked about the draw for the knockout stages, the Scot said: "I would prefer to avoid playing an English team in the next round, I would like to experience new arenas."