Argyle were arguably the better side in the first half after a bright start from the visitors, with Ryan Hardie missing the best chance five minutes from the break on his return from injury.
Schumacher conceded that the Black Cats had improved after the break and said both teams lacked a bit of quality in the final third.
His side face a daunting final two fixtures, travelling to Wigan Athletic on Saturday before MK Dons visit Home Park.
"I think it has been clear for a while it's going to go to the wire," Schumacher said.
"Everybody in the top seven, eight positions in the league are all playing well.
"I felt it was a good game, especially first half. The quality was really high, we passed the ball well.
"We created some good chances and were maybe unfortunate on a couple of occasions not to get the winner, and also a little bit careless on a couple of occasions as well.
"If the pass was a little bit better we might have been in and created a better chance for us to score. The second half was closer, a bit more scrappy, but it's another point in the right direction."
The Plymouth boss felt that in the end the 0-0 scoreline was a fair reflection of the contest.
"I think both teams wanted to try and win," he said.
"It wasn't a negative game, it wasn't two teams who sat back.
"That's not what the two sides are all about. Sunderland have been playing some real good football of late and have been going really well since Alex Neil took charge, and we are the way we are.
"We like to play attacking football so it was always going to be that type of game. I just felt that both teams on the last pass a couple of times just didn't have enough quality to create the goalscoring opportunity that was needed.
"It was a close game, maybe we just edged the first half. The first 45 minutes I felt we were really good.
"The second half we just started a little bit slow and we gave the ball away a few times early on, unnecessarily with sloppy passes, and gave them a little bit of the initiative.
"But then I think as the half went on we came into it again, we grew into the game and it could have gone either way at the end.
"We had a couple of balls flash right across the six-yard box, and one from set play that if someone just gets any touch it goes in. It was a close game, probably a fair result in the game."
Sunderland remain two points behind Argyle in the League One table, having played one game less.
The Black Cats face Cambridge United on home turf on Saturday before finishing the regular campaign against Rotherham United and Morecambe next week.