The Czech winger opted for the digits as a tribute to former club Hearts' 5-1 win over Edinburgh rivals Hibs in the Scottish Cup final. Skacel had been training with his old club - who are now under a transfer embargo until Christmas - before penning a short-term deal with United on Friday.
Houston claims he had no idea of the significance of the squad number until it was too late.
Speaking after a 1-0 win over St Mirren in the SPL, he said: "It's not my style to upset people. I said there were a few numbers available and he asked for 51.
"Call me naive but Gary Hooper wears 88 and Victor Wanyama wears 67 and I never thought of 51 being 5-1. Trust me when I say that.
"It's registered straight away and, once you register it, you can't go back on it. I apologise to the Hibs fans. If I'd known, I wouldn't have given him the number. I'm not in the habit of trying to wind people up or noise other clubs up. Hibs are a fantastic club."
Skacel came off the bench for the final 25 minutes in Paisley, with a Johnny Russell penalty in the second half securing the narrow win.
Houston added: "We've got Rudi until the end of January. I'm sure he's a player we'd like to keep. He was brilliant in negotiations, he's on nowhere near the kind of money he was probably on at Hearts. All he wants to do is play.
"Where I've got it wrong is letting him pick the 51 without switching on to it."