Neil Lennon was "encouraged" despite his Celtic side being overcome by Serie A leaders AC Milan in their Europa League group stage opener in Glasgow.
The hosts started brightly after Saturday's abject Old Firm defeat, but were chastened by easy scores for Rade Krunic and Brahim Diaz.
Lennon's men rallied after two half-time changes, with substitute Mohamed Elyounoussi's header giving the Scottish champions hope before Jens Petter Hauge nipped in late on to secure the win for the Rossoneri.
"It was markedly better than the weekend. It was encouraging," said the Celtic manager. "I don't like losing but there were a lot of good signs for me.
"I wanted an improvement and we got a big improvement. Part of me is quite pleased with that.
"We could have shied away from it all after the criticism we have taken and I have taken but they showed their personality in the second half."
The alarm bells were ringing for Celtic fans after the weekend loss, a game in which they failed to register a shot on target. With that in mind, breaching a Serie A defence looked a tough ask.
While Patryk Klimala was trusted at the weekend, Lennon called upon Albian Ajeti and Leigh Griffiths in attack here, but neither was afforded the service to make an impact during a glum first half.
Too often good positions were not capitalised upon, with Milan showing Celtic how it is done at the other end.
Samu Castillejo was given time to float in a teasing cross that Shane Duffy got caught under. Young defender Stephen Welsh was not close enough to Krunic, and the Bosnian glanced in the opener after 14 minutes.
Zlatan Ibrahimovic's European debut came 19 years ago against Celtic for Ajax, but the Sweden legend had to settle for a role in the build-up to a flowing second.
He started the move as Milan swarmed towards a retreating Celtic defence and the ball was fed to Diaz. Duffy did not get close enough as Callum McGregor attempted to help, but the Spaniard's cool finish bypassed them both to make it two.
The Italians were cruising and Celtic needed a response. Lennon managed to conjure it with Ryan Christie and Elyounoussi coming off the bench at the break. Their spark, coupled with a switch to four at the back later in the half, changed this game as Milan began to creak.
The impressive Diego Laxalt volleyed just over in a warning shot, before Elyounoussi's short run and header from a Christie corner stirred hopes of a comeback. One can only imagine the response if Celtic Park was not lying empty.
With just over 10 minutes to play, Milan quivered and retreated. Celtic probed and pushed, but could not find a leveller their second-half display may just about have deserved.
Instead, Hauge's injury-time goal on the breakaway was a harsh blow as Celtic's group campaign commenced with a defeat.
Man of the match - Diego Laxalt
What did we learn?
That Celtic have a squad capable of changing games. They were far from their best in the first half but seemed revitalised the more the game wore on.
So much of that will come down to the injection of creativity added by Christie. Olivier Ntcham also responded well with the introduction of Tom Rogic and Elyounoussi.
However, there still remains causes for concern. In the first period, Celtic often looked shaky, and the continued absence of Odsonne Edouard - who is still recovering from Covid-19 - there is no ready-made replacement Lennon can rely on.
Celtic have lost each of their last four games against AC Milan, three times in the Champions League before this defeat.
AC Milan's last two shots in this match were their second and third goals, which were in the 42nd and 92nd minute respectively.
Elyounoussi has been directly involved in seven goals in 10 Europa League group stage appearances (five goals, two assists).
Krunic scored his first goal for AC Milan in his 25th appearance for the club. He also became the first Bosnian player to score a European goal for Milan.
Ibrahimovic (39y 19d) became the oldest outfield player to start a European match for AC Milan since Paolo Maldini (40y 245d) in February 2009 against Werder Bremen.
Celtic will attempt to get back to winning ways in the Scottish Premiership, but face a tricky visit to Aberdeen (12:00 GMT). A trip to Lille next Thursday provides the next Europa League test.