Stanley dominated the League Two contest for most of the first hour, but could find no answer to Billy Kee's early goal against his former club.
It took Kee only 10 minutes to open the scoring from 10 yards after a crisp exchange of passes with fellow striker Calvin Zola inside the box.
Summerfield said: "Keeping a clean sheet was a big priority for us. We thought we would get a goal somewhere and defensively I thought we played very well.
"Accrington had a lot of possession, but they didn't have the goal and we did. We showed last week (at Crewe) how resilient we can be when we've got something to hang on to - and we did again as a team.
"We were a bit disappointed we didn't do a bit more attacking-wise in the first half, but the wind didn't help us like it didn't help them second half.
"But I thought we did start to get a little bit more shape and possession in their half and actually created a few more chances for ourselves."
Accrington looked much the brighter team in the first half, but Burton had chances to increase their lead. Skipper Zander Diamond could only poke a Kee flick straight at goalkeeper Paul Rachubka and the defender also headed narrowly wide after stealing on the end of a Chris Palmer free-kick.
Kee also went close with a 15-yard shot, while Stanley were unable to turn their superior possession into scoring opportunities.
Burton keeper Dean Lyness had to back-pedal to tip a huge clearance from his opposite number over the crossbar and also did well to push a skidding Luke Joyce shot round a post.