United's centre-back partnership of Harry Maguire and Victor Lindelof came under fire following their display against Palace, with the 3-1 defeat highlighting the club's need for a more dynamic presence in defence.
A knee injury limited Bailly to 11 appearances last season but the Ivorian looked assured in United's 3-0 victory against Luton Town in the League Cup on Tuesday.
"Eric is fit again, a big, big plus and looking forward to seeing him develop and play more games. We've been waiting him to be fit and play more regularly," Solskjaer said ahead of Saturday's trip to Brighton.
"I think last season proved to us how we can defend at our best, last week wasn't fantastic, we conceded sloppy goals, but I think our defensive record from last season with Eric and Harry shows how good a partnership they were."
Saturday's game will be the first of a double header against Brighton, with United set to visit the Amex Stadium for their League Cup fourth-round tie next week.
"We have to take it one game at a time, the Premier League first and all our focus is on that. We had a bad start last week and we want kick on and play a better game," Solskjaer added.