The second-round replay, which was played on a difficult playing surface at the Kassam, made harder by its frequent use by London Welsh rugby club, was won 2-0 thanks to second-half goals from James Constable and Peter Leven.
"We try to play football but the pitch made that very hard and then you have to go a bit longer," the U's assistant manager said.
"We stuck at it, we wore them down and we're through to the third round.
"It was pretty tight in the first half, but as the game wore on I thought we were looking the more likely to score.
"The pitch was difficult for both teams. The important thing was winning the game and getting through to the next round."
The 2-0 victory means Oxford are now unbeaten in six games and will host Sheffield United in their first third-round tie since 2002/03.
"I think we were very professional," Lewis added. "They're a good bunch of professionals who keep churning out results.
"It was great to see Peter Leven back to his best as well. He's finding his way back in, because he missed pre-season and the first part of the season through injury.
"But he made one and scored one and it's great to have him back in and playing like that because he's a very good player."