The Royals took the lead twice but United came out on top thanks to goals from Anderson, a Wayne Rooney double and Robin Van Persie, in a thrilling first half.
The result leaves Reading in the relegation zone after three back-to-back defeats but Tabb believes that his side are capable of getting themselves out of trouble.
He said: "It's disappointing - but we are scoring goals. It seems like when we're solid and don't concede we don't score - but when we do score we concede a few.
"We've got to put our finger on the fine lines. I'm sure if we can have a good little run we'll climb out of where we are. We're looking like we can do that but we just need to iron out one or two things.
"We had the ball a lot, we passed it more and were adventurous - but that leaves you open at the back so it's a real tough one.
"The neutrals at home would have been delighted with it as it was a bit of a thriller - especially the first half."
Tabb's team-mate Adrian Mariappa was also disappointed not to take anything from Saturday's game, and he thinks that the Royals can take heart from their performance.
"We put them under a lot of pressure so we're disappointed not to come out with anything," said Mariappa.
"We played some great football against, in my opinion, the best team in English football. You want to test yourself against the best players in the world and they had a lot of world class players.
"I thought, as a team, everyone acquitted themselves really well and I think you see that we thrive playing against players like that as we raise our game. All we need to do now is take this in to the coming weeks."