Jordan Chidley, 25, rushed onto the pitch just after Chelsea winger Mykhailo Mudryk had scored an injury-time equaliser to push the tie to penalties.
Chelsea, who had been trailing thanks to a goal from Newcastle striker Callum Wilson, went on to win the shootout 4-2. They are set to face Liverpool later this month in the final of the competition.
Chidley, of Wren Road in Sidcup, was charged with common assault on Dubravka at the Stamford Bridge match on December 19 last year. He faced an allegation of going on to a playing area at a football match without lawful authority.
Appearing in the dock at Westminster magistrates court on Thursday afternoon, Chidley pleaded guilty to both charges.
District Judge Neeta Minhas handed him a three-year football banning order and a fine of £807.
Prosecutor Malachy Pakenham told the court that Chidley climbed down onto the pitch after the goal and ran over to Dubravka.
“The steward tries to grab him, he then puts his arms out and grabs and touches the goalie who pulls away from him,” Mr Pakenham said.
The prosecutor told the court the contact was “quite minimal”.
When arrested, Chidley said his behaviour was “due to overexuberant celebrations” and the fact that Chelsea had scored in the final minutes of the match, the court heard.
He insisted the incident was not “malicious” but “was just euphoria”.
The judge made reference to the “extremely positive” character references given for Chidley.
But she told him: “When I’m sentencing you I’m thinking not only about the offence that was committed, but also … I want to send out a message to deter other people from doing something similar.”
Wearing a black suit, Chidley nodded in the dock as he listened to the judge.
He was fined £807, ordered to pay a victim surcharge of £323 and costs of £85 – totalling £1,215After the match, Chelsea boss Mauricio Pochettino and Newcastle’s Eddie Howe both spoke out about the incident.
“I have always said that the safety of players, coaches, managers, referees, linesmen that’s the priority in any football match so more has to be done to keep especially irate supporters away from the pitch”, said Mr Howe.
Pochettino added: “We need to be careful. The fans need to be careful with this type of thing because it’s a thing that can put in danger the players. I’m disappointed.
“I don’t agree with this type of thing that happened here in Stamford Bridge and in other stadiums in England or around the world. It’s always disappointing with this type of thing because it’s dangerous.”