Defender Ofuso Appiah clattered into the 22-year-old in the closing stages of the Europa League qualifier.
It left a sour note on an afternoon when Hearts won 6-3 on aggregate.
"I was really disappointed with it and I think the referee got done," Neilson told BBC Scotland.
"Jack's got the ball in his hands and the boy comes in and smashes him then goes down and plays dead so he doesn't get booked.
"These challenges shouldn't be allowed in football. That wasn't acceptable today."
Callum Paterson and Igor Rossi had Hearts 2-0 ahead within the opening eight minutes before Alim Ozturk made it three.
Ozturk then sliced into his own net, but Rossi soon restored Hearts' three-goal lead before a strike from Vladimir Voskoboinikov.
Hearts will now face Birkirkara of Malta next week in the second qualifying round.
"We showed a real sharpness in the first half, something we missed last week fitness wise," said Neilson.
"We tired around the 60th minute, but hopefully this game has helped us and we can get geared up for Malta next week.
"We knew we could get at them. The work rate from the players was fantastic.
"To have such a hard game last week with the expectation of it and then to come here tonight and go and perform like that was great.
"We're still in pre-season. Generally it's six week and we're only three weeks in."
Neilson warned that Birkirkara will not be a walkover and pointed to them taking West Ham United to penalties in last season's Europa League qualifiers.
"They're a good team, they're a very good team," he explained. "You think when you're going to Malta with a Scottish team you should be winning, but they're invested a lot of money, they had a great result last year against West Ham, they've got some real quality players."
Hearts head coach Robbie Neilson labelled a challenge on Jack Hamilton unacceptable after the young goalkeeper was left needing stitches after the 4-2 win over Infonet Tallinn.