The Welsh region top the GUINNESS PRO12 table, after their 62-13 triumph at the Liberty Stadium maintained their 100 per cent winning start to the season.
Webb touched down twice, while there were tries too for Jonathan Spratt, Dan Baker, Dan Biggar, Hanno Dirksen, Tom Grabham, Tyler Aldron and Jeff Hassler.
Yet, keen not to rest on their laurels, Webb wants Ospreys to up their game further if they are to mount a successful title challenge for the first time since 2012.
"It was an impressive performance, but we still have a lot to work on," said the 25-year-old.
"We could have been more clinical on a couple of occasions, our exit strategies were sloppy and we conceded a silly try.
"It will be a much tougher test against Munster [on Saturday]. There is no reason why we can't go there and get the win but we need to be clinical."
Webb opened the scoring in Swansea, gathering the ball on the halfway line before piercing through the Edinburgh defence and touching down under the posts.
He later added a second to take his try tally for the season to four - already eclipsing the number scored in each of the last two seasons.
"It's the best try I have scored," added the Wales international, of his second-minute try.
"But, hopefully, there's more to come.
"It was a great start for me. I just thought I should pin my ears back and go.
"I did not have any support, so there was just one way I was going and that was over the try line."
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