Stanley dominated the npower League Two contest for most of the first hour, but could find no answer to Billy Kee's early goal against his former club. Beattie might have made all the difference but had to be pulled from the team after picking up an injury in the warm-up.
Richardson said: "I don't think we deserved to lose the game in respect of our good possession. We got into good areas and the only thing that was lacking was that we needed to be a bit more clinical."
The Stanley boss continued: "Unfortunately, you don't win football games with possession and you don't win them with chances on goal. You win games by putting the ball in the back of the net - and Burton beat us on that score.
"Their goal came against the run of play, but you have to deal with setbacks like that, but all we did was knock on the door without managing to score. It was disappointing that we worked so hard to get in good areas without making the most of them.
"Obviously James Beattie was a big miss for us, but he felt something in the warm-up and I decided to pull him out of the team rather than run the risk of him possibly missing more games."
Burton assistant manager Kevin 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 big 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."