The Baggies chief was hopeful that his side could continue the form which had seen them win three successive Premier League matches going into the game at Old Trafford.
However, Wayne Rooney's strike nine minutes before half time left them with work to do, before Jonas Olsson's first red card in the Premier League for two bookable offences on 66 minutes left them with a mountain to climb.
Midfielder Keith Andrews dropped back into defence to cover for Olsson and he brought down Ashley Young in the area five minutes later which enabled Rooney to score his second goal of the game to seal the points for Sir Alex Ferguson's side.
"We made a good fist of the first half until Rooney's goal," said Hodgson to the club's website.
"We were working hard to contain United.
"I didn't think we were attacking them well during that period.
"When we won the ball back, we tended to lose it quickly and too easily.
"But certainly we were making life difficult for United and keeping them at bay.
"But when Rooney scored that was always going to change the complexion of the game to some extent.
"The second half was going to be harder and then going down to ten men, and while being down to ten men having to change our back-four by putting a midfield player in at right-back, we ended up conceding the second goal."
He added: "I think I can commend the West Brom players for the effort they put in.
"There were plenty of tired legs out there but they never gave up and never stopped fighting, albeit we had to live dangerously a few times when the ball was buzzing around our penalty area."