Tries from Alex Dunbar and Duncan Weir helped the Warriors to an 18-15 win at Rodney Parade and moved them up to fifth in the PRO12 table.
Gregor told glasgowwarriors.org: "We had to play much better in the second period so that we could win as we didn't perform well in the first half.
"We stepped up in the set piece and defensively we got a lot better.
"We came out in the second half with much more resolve, determination and we were more direct which led to Alex Dunbar's try.
"We did enough to win but we put ourselves in a tricky situation after the first half.
"At half-time we spoke about fronting up as we weren't listening to the referee on a couple of occasions and we didn't look after ball.
"Gordon Reid performed a great turnover later on which illustrated how much we improved.
"Alex played well and was always looking to win the tackle contest. His run was excellent, picking up the ball from Mike Blair who also played well on his return.
"The players are delighted and the win helps boost us up the table a little more with eight games to go.
"We've got Cardiff at home in 10 days so we know that if we keep on winning we'll put pressure on those teams in the top four."