The visitors faded badly having gone ahead in the seventh minute through Fernando Torres, his third goal in four days and first away from home since March 21.
Hugo Rodallega equalised in the 52nd minute and the Latics looked the better side in the second half, although Steven Gerrard had a shot crash back off the crossbar late on.
"We didn't deserve to win the game. I thought we looked tired, our passing was not anywhere near where we expect it to be," said Hodgson. "We had a bright start and bright finish but I think we can be more than happy with a point.
"The goal was a wonderful piece of play from two outstanding players, a marvellous pass and a wonderful finish which put us on the front foot.
"But we didn't capitalise on that. We had a spell where we were pretty much in control but from the start of the second half we invited Wigan on to us all the time by consistently giving the ball away.
"As a result they took advantage and scored an equalising goal. We did a little better towards the end and we were unlucky with Steven's shot which hit the underside of the crossbar.
"But it would have been harsh on Wigan had we won it and they can probably feel the 1-1 result flatters us more than them."
Hodgson named the same side which beat Chelsea 2-0 on Sunday but the players tired quickly and they were not helped by Raul Meireles battling through the first half with sickness before being replaced at half-time.
"You can put it down to Napoli, Blackburn, Bolton and Chelsea with a small squad of players," said the Reds boss in reference to a succession of games in a short period of time.
"We have got five injuries at the moment, that is what we have and are using.
"Meireles was sick. I don't know how long it will take him to recover but he was complaining of it just before the game.
"He wanted to play and took some tablets and that got him through the first half but there was no option but to bring him off.
"Hopefully we will get some players back soon and that will help us.
"Now we have to work hard to get people back in the right physical and mental frame of mind.
"We always knew this was going to be a tough test, they are not a bad team at all."
Wigan manager Roberto Martinez was delighted with his side's display.
"The first 15 minutes we were not in the game at all and we got heavily punished as you would expect against world-class players," he said.
"But after that I was extremely pleased with the way we controlled the game, imposed ourselves and created chances.
"You feel when you do that against Liverpool you expect to get the reward of three points.
"I am extremely proud of the players. It would have been very easy to feel sorry about themselves and allow Liverpool to win the game.
"They are really disappointed and frustrated in the dressing room and that fills me with pride and it shows you the characters we have at this club."