United matched their visitors for endeavor, but two goals from £10.5m striker Juan Pablo Angel were enough to send the Villans into the third round of the competition.
Laws said: "We really stretched them. There was a fair few million pounds worth of talent out there but credit to our lads, we played to the best of our ability.
"We don't give up, they keep going, the crowd got behind them and I thought the response was positive.
"We wanted to get the ball but the quality final pass let us down, but that's just naivety and they will become better players.
"We've given it our best shot but, as all managers say at this time, we'll concentrate on the league."
Aston Villa manager Martin O'Neill said: "I suppose it's easy to be gracious after the game, but you have got to give them great credit.
"We had to match that enthusiasm that they showed.
"When we had some very good chances at one stage to put the game beyond them we weren't able to do that.
"Scunthorpe were always in with a chance and if the game had gone on another few minutes, you just don't know what would have happened."