The newly-promoted Tigers, who stunned champions Leicester City on the opening day of the campaign, grabbed their second consecutive win thanks to late goals from substitute Shaun Maloney and Abel Hernandez.
The result means that Hull maintain a perfect start to the season despite a troubled off-season which has left them with no permanent manager and just 13 fit senior players.
Phelan told Sky Sports News after the game: "This Premier League can be brutal but at the moment we are riding a bit of a wave. Credit to everybody working at this football club and credit to the players for the effort they've put in.
"We knew the quality Swansea had, we knew that they would keep possession really well. We decided, do we chase that? Or do we just stay compact and save some energy? Overall, I felt the players' commitment, their effort and their discipline was really good, and it paid off for us.
"We've inspired Hull. Not just as a football club but as a city. It's given them a little bit of belief. There are a lot more games to go but in the past two weeks we've put some smiles on their faces."
The result puts the Tigers third in the Premier League table.