Brede Hangeland's first-half header, following a period of intense pressure from the 2009 UEFA Cup winners, sent Fulham through to the last 16 of the revamped competition for the first time in their history.
Jadson pulled a goal back but Fulham, 2-1 first-leg winners at Craven Cottage, held out for a 3-2 aggregate victory. But the evening was marred by an Achilles injury to striker Bobby Zamora and the late sending-off of skipper Danny Murphy, whose kick at Darijo Srna will see him miss the next match against Juventus.
"The only thing that marred the even was the sending-off of Danny Murphy, who had a very good game and will now miss the next game," said Hodgson, who also apologised for his touchline rant after a foul by Shakhtar's Douglas on Damien Duff.
"I thought it was a bad foul on Damien Duff and I was angry he fouled him in that way, but if ever you let your emotions get the better of you it's not good and inexcusable and I made my excuses to the referee.
"Sometimes things happen to make the red mist to fall, but I'm thankful no further damage has been done."
Hodgson rated Zamora, who worked as hard as ever as the lone striker, as doubtful for Sunday's trip to Sunderland.
Nonetheless, Hodgson was full of praise for his side.
"It has been a wonderful night for the club," he added.
"Shakhtar showed what a good team they are. Their ability to pass and keep the ball is as good as I've seen in my 35-year career.
"I don't like to compare nights, but it's yet another marvellous night along the way and great credit to the team. I really enjoyed the night and the performance but I still hope they'll be some more good nights to come. I'll wait until I retire to discuss which were the great moments and which were the lesser moments."