The Sale player went on at the Millennium Stadium when Scotland's defeat was inevitable but managed to help limit the damage in the later stages.
White, who won his 33rd cap in Cardiff, is keen to establish himself again as a first-team player.
He said: "I prefer to be in the starting line up but that's the way it is in rugby nowadays. It's a 22-man squad and you have to be able to come on and make an impact.
"That's what Matt Williams asked me to do and I managed to make a contribution.
"I wasn't surprised that I didn't start because you can never take it for granted but I was disappointed.
"Matt said that he saw my role as coming off the bench as an impact player but obviously I see myself as more than just that.
"I had some good tackles but the game was going past us by the time I came on and it would have been better if I had been closer and we were charging for victory."
England travel north as odds-on favourites and White admits Scotland's surprise 19-13 victory in 2000 will mean little when the world champions take the field.
He said: "The only similarity from that game is that England are massive favourites and we are massive underdogs, that's about it.
"The boys were up for it on that day, we harried them and closed them down and had a real belief that we could win.
"But that game has not been mentioned in the training camp. You have to be realistic, they are the best team in the world and you can't get away from that.
"For us to beat them on Saturday we have to be at our best."