Szmodics left for Championship side Blackburn Rovers on Monday in a deal that could eventually be worth £2.5 million to Posh.
Posh boss Grant McCann was disappointed to lose his 26 year-old football, but he accepts the deal was good for his club and for a popular player.
It’s unlikely Posh will sign his replacement before Saturday’s League One home game with Morecambe.
"We have players who can play in Sammie’s position,” McCann stated. “Ben Thompson and Kwame Poku for a start, but we will be trying to bring a player in.
"This transfer has been rumbling on for a while now. I was told about Blackburn’s interest while we were in Portugal and Sammie came to see me and made it clear he wanted to make the move.
"I just told him to keep his head down and keep playing and the transfer would look after itself as soon as the clubs agreed a fee. And to be fair to Sammie he did just that. I spoke to him before the Hull friendly and he wanted to keep playing and he gave everything for the team on Saturday at Cheltenham.
"Some players can be difficult if there is a big move with life-changing money involved, but Sammie wasn’t like that at all.
"I’m disappointed to lose such a good player obviously, but we wish him well. He’s back at the level he deserves to be.
"We knew this move could happen so there have been contingency plans in place, but we won’t rush anything. We still need to make sure any replacement will fit in with what we are trying to do.
"I wouldn’t have thought anything would happen before Saturday’s game.”