Substitute Johnny Heitinga drilled home an injury-time winner after Steven Pienaar's first-half opener had been cancelled out by Marvin Sordell for the npower Championship strugglers.
"It is good to put my best teams out but that might run aground later on if we are running out of legs or we get injured," said Moyes. "There were times I was looking over my shoulder and I didn't have a lot of options."
Moyes said striker Kevin Mirallas sustained a recurrence of a hamstring injury which forced him to be substituted inside the first 20 minutes, but indicated the injury might not be as bad as first feared.
Moyes said: "Kevin has had hamstring problems so we have got to hope it is not too bad, but I don't think it is as bad as we first thought it could be.
"You could see how well we played in the opening 15 minutes and he is a really important player for us. He helped string a lot of things together and we missed him after that - we never really got flowing.
"I thought in the second half we had most of the play without being that creative, but we looked the more likely to score. It was great to get the job done. I've had many years of not getting through in ties quite similar to this."
Bolton boss Dougie Freedman admitted Heitinga's late winner had "kicked us in the teeth", but refused to be too downcast after a performance he labelled the best during his time at the club.
Freedman said: "I am disappointed in the result but not in the performance. We started nervously and they went a goal up, but I felt we handled it and it didn't set us back.
"For the next hour we played possibly the best football since I've been here. We got a deserved goal and pushed everything forward for a winner, then a small detail let us down at the end."
- Sports & Recreation
- Johnny Heitinga
- Kevin Mirallas
- Steven Pienaar
- Marvin Sordell