Danielson was given his marching orders in extra-time for a raised-foot challenge on Artem Besyedin, before Artem Dovbyk’s 120th minute header clinched a 2-1 win in Glasgow.
Sweden had defended resolutely when down to 10 men, appearing desperate for penalties, after arguably being the better side across the 90 minutes of regulation time, having hit the woodwork from the outstanding Emil Forsberg.
Danielson’s red card, which came after a video assistant referee check, shifted the momentum but Andersson refused to blame his defender.
“I have only hugged him,” Andersson told Sweden’s TV4. “This is the worst thing I have experienced in a football context, it was brutal.
“I think we were the better team and to get hit with a sending-off, that’s tough in itself. They fight like they did and then to get knocked out in the closing seconds, it’s so awful and brutal, it doesn’t get any worse when we talk sports.”
Andersson said he initially didn’t feel the sending off was warranted.
Meanwhile, Ukraine progress on to play England in Rome in the quarters, where they will be outsiders.
Ukraine boss Andriy Shevchenko reveled in a famous victory. He said: “Both teams played very well. It was an interesting match.
“Neither side wanted to lose so we got this drama at the end. With this performance and commitment, our team has deserved the love of the whole country.
“We knew how our team should play from the first minutes. We knew who could strengthen us [during the game]. The plan we had developed worked well.”