Richards wants no let-up
Victory saw the Falcons go seven points clear of the bottom-of-the-table Exiles, with two games left in the regular season and just the basement side set to be relegated.
Marcus Watson's first-half breakaway try for the north-east side proved decisive at Kingston Park but former England No.8 Richards knows that with leaders Saracens and Sale their side's next opponents, Newcastle cannot take their top-flight status for granted.
"The job is not done yet," said Richards. "Mathematically, safety is not there. We just have to make sure it is in the last two games."
Meanwhile, London Irish coach Tom Coventry insisted all was not lost for his side, who complete their league campaign against Harlequins and Wasps.
"We created a lot but weren't able to finish which is sign of where we are at the moment," he said. "It's not a hopeless situation, but we have to beat two very good teams now to have any chance of surviving."
Meanwhile, Sale were left eyeing a place in next season's European Champions Cup after moving up to sixth in the table with a 29-17 win at home to Bath.
Victories in their three remaining regular-season league games will seal Sale's spot and the Manchester club's Director of Rugby Steve Diamond said: "If we win our last three games we'll get there. We know where we're at, we know how good we are and we just have to keep building the team."
Will Addison scored one of Sale's four tries and afterwards Diamond said the former England Under-20s wing was deserving of full international honours.
"I thought that Addison was the best player on the pitch so he should hopefully be getting some England recognition if they're watching the games," Diamond said.
Addison was also involved in a nasty-looking clash of heads with Kyle Eastmond that saw the Bath man carried off on a stretcher.
But Bath coach Neal Hatley delivered an encouraging update on the fitness of the England centre, who had only recently returned from injury.
"He took a heavy shot so the good news is that he's up and moving around," Hatley said of Eastmond. "He seems in good spirits in the changing rooms and we'll look after him over the next day or so just to make sure we know exactly where he is."
Agence France-Presse