The Magpies entered their final group-stage fixture at St James' Park needing to beat the Rossoneri as well as hope that Borussia Dortmund avoided defeat against Paris Saint-Germain to secure a top-two finish.
Howe's men were dreaming of a place in the last 16 when Joelinton fired them in front on the 33-minute mark as Dortmund took the lead in their clash against PSG early in the second half.
However, Newcastle's first Champions League campaign for 20 years ended in heartbreaking fashion, as Milan restored parity through Christian Pulisic on the hour mark before substitute Samuel Chukwueze scored with his first touch in the 84th minute to complete the turnaround.
PSG also came from behind to beat Dortmund 2-1 thanks to goals from Warren Zaire-Emery and Kylian Mbappe, meaning the French champions advance to the last 16 with Dortmund, while Milan claim third spot to drop down into the Europa League as Newcastle finish rock bottom and bow out of Europe altogether.
Howe expressed his disappointment at Newcastle's defeat and Champions League exit during a post-match interview with TNT Sports, but nevertheless commended the valiant efforts of his players.
"I thought there were some really good bits, we were dominant at times, but probably needed the second goal," said Howe. "We didn't defend the two goals well enough.
"It was very much end to end. Both teams were desperate to win. We wanted to win the game and we were trying to head for the Champions League so we had to be brave.
"They had to be brave. It made for a very good game. We did create chances and we're absolutely devastated not to go through."
Asked whether the controversial handball decision in their penultimate group-stage fixture against PSG now has a greater impact, Howe said: "I think it would be foolish of me to look back and start bringing up old stuff.
"We had the opportunity tonight to do what we had to do and we didn't take it. We couldn't have tried harder, I don't think we left anything on the pitch."
Howe believes he has learnt "so much" from Newcastle's Champions League campaign, adding: "The value of the squad first and foremost, that's what's exposed us, the fact we haven't had the ability to utilise the squad we've created. We've gone into games very limited in what we can do and that hasn't helped us."
Newcastle have lost each of their last three games in all competitions amidst an injury crisis, and Howe is keen to use those recent setbacks as "fuel" as the club attempts to return to winning ways in the Premier League.
"You always have to use disappointment - the setbacks - as motivation and fuel for your fire to make sure you continue to achieve," said Howe.
"We'll go back to the Premier League and try and do as much as we can to be consistent and stay up there."
Newcastle, who sit seventh in the Premier League table and seven points adrift of the top four, welcome Fulham to St James' Park on Saturday afternoon.