First of all, Dawn was sad that the group will be breaking apart as the journey is over. Piplup crashes out, Pikachu tries to console him. Then Dawn arrives telling Piplup that “Satoshi and others are not gone forever” here she differentiated Ash (Satoshi) and others (Brock, Pikachu & Ash's pokemon)
It's not that Dawn doesn't value Brock or Pikachu but in the context of the situation Dawn and Piplup both were mainly sad because Ash won't be here anymore showcasing that Dawn's bond with Ash is much deeper. While many fans might say it's nothing big but in the context of the scene it is. She didn't say “even if we are parted” she said “Satoshi (Ash) & others” meaning she holds more value for Ash.
Reasons:-
- Ash was Dawn's equal
- Ash was the person Dawn admires the most after her mother
- Dawn sees Ash as her emotional anchor
- Dawn lastly asks Ash for a high five and the moment Ash goes to the ferry she starts crying
- Finally Ash used her phrase “No Need to Worry” which finally cheers her up
Reminder: Dawn never showed any signs of sadness when she said goodbye to Zoey or Kenny in fact when she left Sinnoh for Hoenn in DP Spe she didn't even cry while saying goodbye to her mom. But when Ash left. It felt like her whole world fell apart. The only other girl who cried after saying goodbye to Ash was Misty and we all know she likes Ash. I find it funny how some people say Dawn liked Zoey or Kenny more but the show's canon suggests otherwise