Strachan felt his players created the best of the chances but rued missed opportunities when Hearts bagged two late goals to book their place in Thursday's semi-final draw.
Substitute Andrius Velicka came off the bench after 72 minutes and grabbed the opener just four minutes later, then putting the tie beyond Celtic with his second of the night with five minutes to go.
"We were all right and we felt comfortable in the game," he said. "I couldn't see that coming, it has come as a shock.
"For 70 minutes I thought there was only going to be one winner, I thought we made enough chances and created enough opportunities, we just lacked a cutting edge.
"You need to have a cutting edge in a cup tie but we couldn't take our chances. We only have ourselves to blame.
"They came along, had a good chance and took it."
"I think we can win it," he said. "I knew we could win here and that's what we did. Whoever we get makes for an exciting competition but you can't pick and choose.
"The three teams left would all be strong opposition. They are all doing well and it will be a tough game no matter who we get."