George Ford kicked three penalties and a conversion with Anthony Perenise crossing the line from a rolling maul and a late penalty try sealing the win for Bath, as the home side failed to master the wind and rain in the season's opener.
The match marked the return of Richards to the Premiership or the first time in four years, after he navigated Newcastle's promotion at the first time of asking following a three-year worldwide ban in the wake of the Bloodgate scandal at Harlequins.
However, the game was to end in a humbling defeat, with Newcastle unable to score a point against the side now coached by former Falcons chiefs Gary Gold and Mike Ford.
"We got ourselves into the right positions at times but we managed to shoot ourselves in the foot on occasions but it's something we will take heart from," Richards said.
"We just need to be a bit more clinical in what we do. The first half we didn't take our chances and they went in with points up.
"We didn't have quite the unity of turnovers as we would have hoped and we didn't capitalise on having the elements with us and playing in the right areas as we should have done.
"That's life. You have to learn from these mistakes and we will do."
The game was under some scrutiny following the introduction of new scrum laws in the English top flight, which are being trialled in the northern hemisphere this season.
It was a difficult first test on a windy and soggy night in the north east, and there were some early teething problems - but from them Bath dominated up front, with Newcastle unable to gain a real foothold in the match.
"We had a lot of possession in the first half and we didn't make that possession tell," Richards added.
"It's a long season and it's not about today, it's where we finish at the end of the year. With Quins we came up and it was very difficult. Last season London Welsh had a great start but still went down.
"For us it's what happens over the year and not just tonight."
For Bath coach Ford, his return to the north east ended in a much more positive fashion.
"It's always tough up here and playing in the wind in the first half to go in at 6-0 was a great result for us," he said.
"With them having one chance at goal but not threatening our line at all was good. We just talked about in the second half showing some resolve and some resilience and I think we did all of those things.
"We said we would take 6-3 before the game. It's frustrating because every training session we've had has been in the sun. We haven't been playing a lot of rugby like we saw like that so it's good we had that game management.
"It was freezing for both teams out there but we dominated in the forwards so it's pleasing to get the 21 points and it was pleasing that we didn't concede any."
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