United’s latest inability to make the final of a cup competition at the last hurdle came in the Carabao Cup on Wednesday when they were beaten 2-0 at Old Trafford by Manchester City.
Second half goals from John Stones and Fernandinho saw City edge past United into the final for the second season running.
This marked the fourth time Manchester United has fallen at the semi-final stage of a competition since Solskjaer took charge in December 2018.
Last season they again fell to their city rivals in the Carabao Cup semi-final and lost to Chelsea and Sevilla in the last four of the FA Cup and Europa League respectively.
"Manchester City can score many great goals. You can accept that. When you concede two simple set-plays, it's very disappointing. Just not good enough in those moments," Solskjaer told Sky Sports.
"We didn't create enough big chances. They didn't either. We didn't have the extra finesse we've had in the games lately. We weren't good enough today.
"We played against a very good Manchester City team. They played well. When they play well you have to play very well to beat them. We were just lacking that little bit.
"We're getting closer. This is a much better version of United than a year ago in those semis.
"It's not psychological [losing in four semi-finals]. Sometimes you meet good teams in the semis. We met City who, at the moment, are probably the best team in England."
