Summerfield hails plucky Albion
Celtic manager Neil Lennon has ambitions to manage in the Premier League during his career.
The Parkhead boss has built a good reputation after guiding his club to SPL titles and, this season, a place in the last 16 of the UEFA Champions League.
Lennon remains happy at Celtic but the former Leicester City midfielder also has targets of returning to England's top flight in the future.
He said in the Daily Record: "I'm ambitious and maybe one day, if I'm still good enough, a Premiership team might shine the eyes at me and it would be something to consider.
"I'm very happy here at the minute but who knows? This time last year I was thinking about resigning, because we were 3-0 down at half-time to Kilmarnock and 15 points behind Rangers.
"It's funny how football changes so quickly so I'm aware it can change quickly again.
"I love what I do here and have a great feeling and affinity with the fans and the club. But you never know where football takes you."
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.