The Reds took the lead at Stadion Koln courtesy of a Bruno Fernandes penalty on nine minutes, before the Spanish club restored parity through Suso after 26 minutes.
United then dominated the second half and created lots of chances - 20 shots for the match in total - but the experienced opponents held on and managed to score a decisive goal on 78 minutes via Luuk de Jong.
Shortly after that strike, television footage captured Victor Lindelof and Fernandes in a passionate exchange of views as the Reds regrouped for the semi-final's conclusion.
During the post-match press conference in Germany, Solskjaer was asked for his thoughts on that moment and the manager quickly explained he wants his young squad to have such fire.