The Baggies allowed Steve Bruce's side to come back from two goals down to secure a point, but Hodgson was keen to emphasise the challenge of holding on to an early lead.
"It was too early [to take the lead], we had 90 minutes left to play when we went 2-0 up. So the game starts all over again," he told reporters following the game.
"What it does of course, going 2-0 up, it gives you opportunities because if you defend well your opponents are going to have to come at you and you'll have chances on the counter attack.
"That's what, in actual fact, happened in the first half but I think we should give credit to Sunderland for really mounting a strong challenge, after getting over the disappointment of a poor start both in terms of conceding goals and maybe giving the ball away far more than Steve would like in that early period.
"But they got themselves together again. They got the goal that brought them back into the game at 2-1 and played very well for a spell.
"I think it was up to us to get our minds right again and not to think about the fact we had been 2-0 up but to make sure we got ourselves organised enough to get a result in the second half.
"The result being a draw or a victory. I think we did that reasonably well and that's what was important because we all know the mental aspects of football."
Hodgson added that it was important his players did not dwell on having allowed Sunderland back in to the game.
"Words like squandering opportunities and wasting chances, all these things go through your mind," he conceded.
"You've got to put it out of your mind because if you're not careful you really waste your chance because you can go from 2-0 up to 2-3 or 2-4."
The former Liverpool manager admitted that it was a case of seeing how the game evolved after scoring twice so early.
"You've got to see how the game develops really," he said. "You know in this league wherever you go it's going to be hard to get a victory, like when you're playing at home it's going to be hard to get a victory.
"So I think most of the time you wait and see how the game develops and most important of all you're looking at the performances of your team and trying to make certain you get a performance out of your team.
"That you're attacking as you would like to attack and defending how you would like to defend. I thought our attacking play today was arguably better than our defending play from an organisational point of view.
"But then of course I have a very attack-minded midfield in there with [Graham] Dorrans coming back into the team and [with James] Morrison and [Youssuf] Mulumbu and [Chris] Brunt we have four very attack-minded midfield players."
Albion sit just one point out of the relegation zone after seven matches but Hodgson argued that the table was unrepresentative at this stage of the season, with West Brom having already completed tough fixtures against the likes of Manchester United and Chelsea.
"It's the first three games that have done us in, points we lost at home to Manchester United in a game where I thought we played quite well and could have easily taken a point," he said.
"We did even better at Chelsea, again we were very unlucky not to get anything and the third game where a point was ours we gave it away in the last minute with a ridiculous mix-up between the goalkeeper and the centre-back.
"So at least we could have had one point on the board but we had zero.
"Now we've had three away games with a home game and we've taken five points. I would like to think it's going to take longer than a month or two to make up for those zero points from three games.
"You know that during the season you'll play Man United and Chelsea and chances are you won't get too much."