The victory saw Dean Ryan's men top their group to secure a home tie in the quarter-finals, where they will face 2006 champions Munster.
Lawson believes Gloucester coped well with an Ulster side fired-up by the presence of caretaker coach Steve Williams.
Lawson said: "We just focussed on our own game. Ulster are a dangerous beast and they were out to impress their new coach.
"A team with nothing to play for is always going to be difficult. They are going to give everything a go and fair play to them they did
"We let ourselves down in the last two matches and are glad to get this victory to secure a home tie in the next round. We like playing at Kingsholm of course and it can be important in the Heineken Cup."