The Exiles, newly-promoted from the Championship, overcame Exeter Chiefs 25-24 at the Kassam Stadium to clinch their first top-flight win at the third attempt.
With less than two minutes left No 8 Ed Jackson rounded off a last desperate surge by forcing his way over for the try which replacement fly-half Seb Jewell converted to win the match.
Welsh were heavily beaten in their opening two matches and Jones said: "Two weeks seems a very long time ago since we played Leicester here and were found wanting.
"After having such a tough time against Leicester and at Harlequins, we've learned a lot about ourselves.
"We are delighted not just with the result but the performance was so much better."
Jones has been playing catch-up with his team-building and preparations since Welsh won their legal battle to secure promotion to the Premiership.
They looked to be heading towards another setback when they trailed 14-0 after only 11 minutes but turned the game around.
"We didn't fold," Jones continued. "We kept in there and took our opportunities. We showed a lot of character to come back."
But he knows his side are still a work in progress.
"We don't really know where we are yet. We have some players who haven't been in England for four weeks yet," he said.
"We're a feisty bunch but it does take time. It was important we grew as a team and the win over Exeter, who are a very strong well-drilled side, should improve our confidence."
Exeter director of rugby Rob Baxter, whose side have shocked a number of big-name teams since their promotion to the Premiership in 2010, did not begrudge London Welsh their success.
He said: "We won't be calling a crisis meeting on Monday or calling players in for extra training.
"I think today's more about congratulating London Welsh than worrying about what we did wrong.
"You have to be a decent side to come through the Championship play-off structure and the Premiership is a great place to learn.
"Players and teams get better and London Welsh are doing that. Am I disappointed not to win? Of course I am. We like to win every game of Premiership rugby. I'm probably more disappointed with the way we played, some of the mistakes we made and the way some senior players gave away soft penalties and made wrong decisions.
"We just lost our way. I'm not going to say that over the 80 minutes we deserved to win the game because I'm not sure we did.
"I'm not massively worried about anything because, if there's one thing I know, there's no shame in losing to the promoted side.
"I've seen other Premiership sides lose to Exeter and, all of a sudden, think they need to have a crisis meeting and they can't quite work out why it's crumbling around them.
"We've put in a couple of good performances in the last couple of weeks and we're not a massively different side after today.
"We'll just learn from the things we did wrong, as we do after any other game, and move on."
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