Despite taking a lead through Billy Sharp in the third minute, United saw captain Andy Crosby red carded after 20 minutes and were outfought by the home side.
Laws said: "This was very disappointing, it was our first defeat in a long time and we must pick ourselves up quickly.
"We got a great start with a goal after just two minutes, but when we went down to ten men we knew it was going to be difficult; it was a heavy pitch, and it was taking a lot out of us.
"Blackpool were obviously up for it after their recent troubles, and they gave us a very hard game; it was very physical and we took a few knocks, but we've got a busy programme ahead, and we shall have to cope with that within the squad.”
Grayson said: "At halft-ime I told the lads if this is soccer management, I don't want it, after we went 1-0 down in the first couple of minutes.
"They reacted well and their heads didn't go; and they have my admiration for that.
Two-goal Blackpool hero John Murphy, who hit his 99th and 100th strikes for the club, added: "It has been a funny old week at this club, but then again, this is a funny old game.
"The players had a big bonding session after the departure of Colin Hendry, and we knew we had to put things right on the pitch.
"There is a lot of respect for Simon Grayson, and he prepared us well for the game. We needed three points because there's a bit of a gulf at the bottom.”