A 3-1 home win against play off-bound Swindon was not enough to save them heading back to League Two for the first time in nine years.
"We have got to rebuild again this summer and put the pride back into this club again," said Laws.
"Over the last few years Scunthorpe United have rightly been admired by many people in football for how much they have over-achieved by reaching Championship level. But the last three years have been difficult ones, with now two relegations.
"I know this club inside out and am prepared to do what we have to in order to get it back on track. It will be a difficult job because the finances are very tight and we have to get the wage bill down.
"We have produced some good young players at this club in the past and that is what we have to do again. We do have a crop of good youngsters coming through and we will have to give them their chance with the right mix of some experienced players."
Laws, who returned as manager last November, is likely to have a big clear-out after inheriting a squad that has struggled all season.
He continued: "We did what we had to do in our last match, but unfortunately Carlisle could not do the favour we needed from them by beating Colchester for us. That's not their fault, it's ours for finding ourselves in this position in the first place.
"We have had chances in recent weeks to have been safe, but we have not taken them. The table does not lie. Over the previous 45 games we have not been good enough to stay in League One."
In front of their biggest crowd of the season, Scunthorpe looked to be heading for defeat when James Collins fired Swindon in front after 83 minutes. But midfielder Michael Collins triggered an amazing fightback when he scrambled home an equaliser from a corner four minutes later before Mark Duffy's penalty and a Karl Hawley strike - both in stoppage time - then secured a 3-1 win for the Iron.