Goals from Andy Crosby, a penalty conversion, and Billy Sharp saw the Iron take the lead but they conceded an equliser in the closing stages.
Laws said: "We had to step up 20 per cent after our first-half performance.
"I thought our second half display was outstanding. We quickly got back on level terms, then went in front and the only disappointment is we did not go on and win the game.
"Playing against 10 men is often difficult because it does fire up the opposition.
"But it's our first point on the board, and our second half performance gives us something to build on."
Visiting manager Kenny Jackett was fuming at the decision to send off midfielder Tate.
He blasted: "It was one of a number of colourful decisions that the referee made all night.
"But it's our first point of the season and now we are up and running. I thought we showed some great spirit after going down to 10 men so early in the game.
"There are a lot of positives we can take. The one negative is the injury to skipper Gary Monk - it appears to be knee ligament damage."