Manchester United did everything posible to win the cup final and secure a place in the EL. I think that Chelsea expected a victory from City in the final, this would have given them a place in the EL and perhaps Pochettino’s further fate at Chelsea would have been different, but perhaps with this victory ten Hag retained his place in Manchester (we don’t know this for sure yet). But Chelsea and Manchester United did not have the best season, if a team cannot play in the Champions League, this is a weak result.
I agree with you, if Manchester United and Chelsea cannot play in the Champions League whatever they achieved is a weak result. Chelsea wasn't expecting Manchester United to have victory over City because we all know how strong they are throughout the season, many people were saying that it was a fixed match, and Manchester United was not strong enough to defeat Manchester City. This is a football and everything is possible, Chelsea was performing badly from the beginning of the season, so I wasn't expecting them to play fantastically at the end of the season. Pochettino improved his players and finished the season in the 6th position, hoping to play in the next Europa League if Manchester United lost the FA Cup to City, but that did not work as they thought, and Pochettino got fired.
I don't think Ten Hags will retain his place in Manchester United after winning the FA Cup, but we can see what will happen before the next season since one of the managers has agreed to replace him.