Stoke City boss Tony Pulis was upset with everyone after their 1-1 draw against West Bromwich Albion.
Substitute Carlos Vela equalised from a seemingly offside position in the 87th-minute after Rory Delap's opener and had a glorious chance to win the game deep in stoppage-time.
"We've not played well tonight, it's as poor as we've played all season. But looking at their goal, it's a shocking decision," rapped Pulis.
"If he can't get that decision right what's he doing officiating at our level? We'll just get on with it...our players made bad decisions too."
Hodgson agreed that there may have been a fortunate element to the goal but thought it the least his side deserved.
"Whenever you have a goal like that against you, you consider yourself unlucky. I couldn't say whether or not it was (offside) but whenever you concede that type of goal you have the right to be frustrated or angry.
"With the number of chances we created and the number of opportunities I think one goal is the least we could expect for our efforts."
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