You must not have followed Kagawa´s first weeks at Dortmund if you believe that. The hype around this transfer among the supporters and the media was huge. On top of that there was no time of easing him in because both Reus and Blaszykowski were out injured and everything besides a win at home vs. Freiburg would have been considered a failure.
So here was Kagawa starting after one week of training in front of 80.000 people, who celebrated him as a hero even before the match started and basically expected him to continue right where he left it two years ago. You think that this no pressure for him?
My personal belief is that the pressure of playing for a club like United (or Madrid, Barcelona or Bayern) is greater than that of other clubs. The fans don't just demand Champions League qualification, they demand consistent trophies and a season without silverware is deemed a failure. The difference between a 2nd place finish and last 16 of the Champions League being a good season and having to win the league for it to be deemed a good season are worlds apart in my opinion.
This is before we even contemplate the difference for Kagawa personally, who clearly felt like the step up to United was huge, which is not that surprising when you look at how United are viewed in that part of the world. Just watching him play for the last 2 seasons it was apparent that he was overawed by the environment. He became a shrinking violet, whereas the player's that are usually the most successful at United thrive on the pressure (Ronaldo, Keane, Cantona etc).
It´s hilarious that players like Blind and Herrera are already considered players with stronger characters, because they played well in a system Kagawa would have also excelled in. When you compare both Dortmund and United in their respective last game you will find several similarities. Both faced deep lying defenses and tried to break them up with fast and fluid combination football. Both pressed when the opportunity arised. Furthermore both Blind and Herrera have obviously the backing of the manager, which is something Kagawa never really received after SAF´s retirement. It is not something magical that Kagawa performs better at Dortmund as he did in Manchester for the most time. There are pretty obvious reasons for that.
The reason that the aforementioned player's are already considered stronger characters is because they didn't just thrive when we were playing well, they were the ones that created the tempo for us to play well. This is the difference between a player like Kagawa/Berbatov who shine when you would win 4-0 regardless and other player's who are the reason behind that kind of performance in the first place. It is easy to get an assist or goal when everyone around you is playing well (which was Kagawa's M.O. at United). The tests for Herrera and Blind are still to come, I want to see them create that tempo on a regular basis, if they do so within a matter of games they'll have surpassed Kagawa's contribution. The difference between Mata and Kagawa is also stark in my opinion. The latter is a fair weather player who only looked competent when we were winning, Mata's stats in this regard speak for themselves (irrespective of team performances).
Coming back to the expectations to the club. What do people think the audiences and media expect from Dortmund in Germany? We are supposed to be the challenger of the top dog and the team to keep the title race interesting as long as possible. If we don´t manage that for whatever reasons our league seasons are never rated as better than decent no matter the circumstances. We are part of our league´s title race as much as you guys are supposed to be. You might have bigger expectations in the CL in the long run, but outside of a monster draw in the round of 16 anything less than top 8 would also be considered a failure on our part. If top 8 in Europe and title challenger in a European top league is not considered the absolute top level, then what is?
The biggest difference is that despite the level of football we have established on the pitch in the last few years, which resulted in the before mentioned expectations, we are not as big as a lot of our competition and can´t throw massive amounts of money on the market to solve our problems and keep key players with premium wages. We have to find other ways to keep the machine running.
Dortmund are the Arsenal of German Football. There is absolutely no pressure on them to win the Bundesliga. If they finish second every season for the next 5 years, be the losing finalists a few times in the cup and reach the last 16 of the CL, Klopp will keep his job and still be adored by the fans. At United a manager that doesn't win trophies for 5 years would be getting the sack, no ifs, buts or maybes.
Dortmund are a great club and I love the way they play and what they've done with the resources available. Klopp is an absolute genius to have gotten them to where he has with their budget and you'll benefit from him for decades. Also the way things are going financially for yourselves there is no reason in the future why you can't start to compete with top tier clubs (particular with the Commercial deals available in Germany). However lets not pretend the pressure is anything like as fierce.
Just look at the difference between what constitutes a good season for Guardiola vs Klopp. Anything but consistent success is deemed abject failure for the former. The latter has copious amounts of breathing space. Stating injuries last term as a reason you weren't as successful is accepted at Dortmund, at Bayern it just isn't. The fact that Klopp's job isn't starting to get under pressure after the last 2 seasons without silverware is testament to this, Guardiola with the same last 2 seasons would be under big pressure, you must see this?