Burrell and May grabbed all the tries in the four-try, 31-14, Kassam Stadium success that took the Saints one step closer to the Aviva Premiership Rugby semi-finals.
Saints remain fourth in the table with two rounds to play, five points ahead of fifth-placed Gloucester and nine in front of Exeter in sixth. This means that any kind of victory over Sale Sharks at Franklin's Gardens next weekend would see the Saints in the play-offs for an unprecedented fourth successive season, but Mallinder says that the team will have to tighten things up compared to the win over Welsh.
"It was a loose game," Mallinder told the assembled press after the game. "London Welsh came out to play with ambition, and so did we. I'm pleased with our attacking intent but we've got to tighten things up a bit in defence.
"Luther Burrell came in today and played well, and Tom May came on and did a cracking job. We'd talked about their line speed and Tom's tries came at a good time for us.
"We forced things a little bit too much and had we kept things a bit tighter we could have scored a few more tries. But in the end it's a job well done.
"It's put us in a good position, and if we beat Sale next week it'll help our top four ambitions.
"We need to go out on a high at home. Our away form has been better than our home form, which is unusual for us, and we'll need to be up for it against Sale."
The result also confirmed the Exiles' relegation from the Aviva Premiership, with Mallinder adding: "Welsh have been a credit to the Premiership and pushed teams close. They've come in and tried to play some rugby."
And the Saints boss also thanked the team's supporters for their showing in Oxford. The declared crowd was just over 5,100, with many observers reckoning that over half were wearing black, green and gold.
"I thought the travelling fans were superb today," Mallinder commented. "It's not a long way from Northampton to Oxford but it still takes commitment to make an away trip. They made lots of noise and made their presence felt."
The Saints round off their 2012/13 home Aviva Premiership Rugby campaign next Saturday evening against Sale Sharks. Kick off is at 5:45pm and although tickets remain available they are selling quickly.
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