"We could have won although could've, would've, should've doesn't wash - leaders need to step up to drive things forward," Lawrie told the Scotsman. "Everybody has to have a bit of belief. We are not panicking. We are not divided or anything like that.
"At the minute we are in a position in the league where we don't want to be and it is going to take character. We need to step up and get it sorted.
"When things are going wrong we need to come together, have a look at the areas that are going well, look at what is not going right, correct them, and get the ship going forward again. That is two bad defeats to be honest. There is no way of dressing that up.
"I am so gutted for the fans and the staff who put the graft in at the stadium. The fans want to see you have a bit of fire about you and we didn't show that enough."
Lawrie came on as a replacement with 11 minutes remaining, more than a year after he injured his knee in training on December 18, 2011.
"Yes, I was chuffed to get back after the journey I have been through," said the Scotland Sevens star, who also has two caps for Scotland A. "It was all there at the end but it took us 60 minutes to get going. A crowd like that deserved so much better.
"I was just dying to play all week and then Edinburgh don't turn up until the last 20 minutes. It's hugely disappointing. We have to take the positives because there is a game next week, we look at what we did well.
"When we scrummed well, when we won our lineout, when we played good areas and did sensible things, when we didn't put ourselves under pressure we looked a threat, but, ultimately, we didn't do that for long enough in the game. I am always magnanimous - fair play to Glasgow but we need to look at ourselves and regroup."
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