Mussels exited the Sussex Senior Cup 6-3 at local rivals Steyning Town last Wednesday and then lost 5-3 at high-flying Ringmer in County League Division 1 on Saturday.
MacMillan is due back from an ankle ligament injury in two weeks and that cannot come soon enough for Burt, who said: “We’re letting in far too many goals at the moment but we’re missing Ryan big time.
“He’s a great player, who wins tackles, has pace and is good in the air. If he was playing, we wouldn’t be conceding so many.
“He’s started to do a bit of running, so, hopefully, he will be back in a couple of weeks.”
Despite the defeat to Ringmer, Burt took positives out of the performance as Mussels showed character to get two late goals back, having trailed 5-1 midway through the second half.
A Lee Wood free kick slid under Mussels keeper James Shaw’s body to give the hosts a eighth-minute lead but Mussels levelled seven minutes later when Mark Pulling fired home from 25 yards.
Shoreham then passed the ball well, until Ringmer went back ahead when Marc Whiteman struck when a corner was not cleared.
Aaron MacMillan got through early in the second half but his shot was pushed on to the post by the Ringmer keeper and the home side quickly made Shoreham pay.
Whiteman got his second on 54 minutes, before the lively Aaron Watson, who caused Shoreham problems throughout, made it 4-1 three minutes later.
An own goal gifted Ringmer a fifth, before Shoreham fought back and pulled goals back when Pulling again struck from 25 yards and Jon Melia bundled the ball home.
Burt said: “I was reasonably pleased with the performance but we just let too many goals in.
“Aaron Watson was excellent for them and is the best player in the league. He’s very tricky and we tried to double up on him but he’d just go past two or three players at a time.
“We conceded five goals and lost, so I’m not over the moon. But there team is packed with quality and there were positives to come out of the game for us.
Shoreham host fifth-from-bottom Hailsham on Saturday and Burt said: “It’s a big game. Our aim is to finish as high as we can.
“We’ve got to keep beating the six or seven sides below us to stay in front of them.”