The League One side triumphed 4-1 in the spot-kicks after the Capital One Cup tie ended in a 2-2 draw after extra time at The Den.
Crawly were denied victory inside 90 minutes by Shaun Batt's late equalier for the Lions, but the visitors made no mistake in the shoot-out.
"I thought it was a deserved victory in the end," Baker said afterwards. "We deserved to win it in normal time and probably almost in extra time, to be fair.
"Sometimes you get a bit of justice in penalty shoot-outs and we did in the end.
"They didn't stop doing what we had done all night, which was pass the ball around and work extremely hard and be disciplined in our shape. We did all of that and to do that for two hours away at a Championship side speaks volumes for the players."