Xavier Simons and Max Conway were denied by the woodwork either side of half time, while Corey Addai made some big saves.
Both of the hosts’ goals were sucker punches at the end of the respective halves as the Whites left Edgeley Park empty-handed.
“Disappointing, obviously, to lose the game,” Schumacher said after the final whistle. “I thought it was a game that we probably didn’t deserve to lose.
“I felt we created a lot of opportunities again, went to some brilliant areas and didn’t make the most of them.
“The two moments that mattered, they’ve been more clinical than we have again. So disappointing to lose it, but enough positivity in there that against a really good team, we created well enough to win the game.”
The head coach continued: “I thought the performance was OK. We know we were against a good side who pass and move the ball really well.
“I felt as though we were in control of all those situations. We didn’t feel under pressure from many moments and got into some really good areas from our attacking point of view.
“What we spoke about in the week, we haven’t managed to take them. The keeper has made a couple of good saves, granted, but we’ve also missed the target from areas where we can’t miss the target. That’s the most disappointing thing – we don’t do enough with our good play.”
Teddy Sharman-Lowe, Xavier Simons, Amario Cozier-Duberry and Mason Burstow were handed their debuts and Max Conway got the nod following his impressive loan spell at Crewe Alexandra last season.
Despite the result, Schumacher felt there were some bright signs from the new additions to his squad.
“It’s hard to say that when you’ve lost but, again, there is positivity in the actual way we played,” he added.
“The new lads are all settled in and trying hard, and it feels like they have been here a while so that is OK.
“But as I said, we have got to do better because in these big games, in tight games, you have got to be clinical.”
Conway had a penalty shout turned down by referee Elliot Bell in the first half after a driving run into the box.
There was also a controversial free kick awarded after Bolton thought they had won back possession high up the pitch and played in Carlos Mendes Gomes on the left.
When asked about the decisions, Schumacher replied: “From the first minute really, there was a real soft foul when we nicked the ball off Ollie Norwood.
“A few minutes later, Mason Burstow got pulled back and I said to the fourth official, ‘If he is going to give soft ones, that’s the same’.
“I just felt we didn’t get the rub of the green from that moment. But I don’t like moaning about refs, it’s about what we’re doing.”