Pep Guardiola said he feared future problems after a fan ran on to the pitch and jostled Oleksandr Zinchenko during Manchester City's 3-2 FA Cup win at Swansea City on Saturday evening.
Three juveniles were arrested and held in custody by police following two separate incidents for encroachment onto the pitch, two Swansea fans and one Manchester City fan, Sky Sports News understands.
A supporter from a home stand accosted Manchester City substitute Zinchenko, and Guardiola admitted it was a concern.
He said: "It's happened a few times lately and it's a worry because in the future we could have problems.
"It's not nice but thankfully nothing happened this time."
In a statement, South Wales Police match commander Superintendent Steve Jones, said: "The safety of supporters, players, officials and those who work these games is paramount.
"Those who invade the playing area are committing a criminal offence, will be dealt with robustly and could face lengthy bans from all football matches.
"We will continue to work with the football club to prevent and deter this unacceptable behaviour from a very small minority continuing."
Earlier in the day, seven supporters were arrested at Bournemouth, including a 14-year-old boy, as visiting fans spilled on to the Vitality Stadium pitch while celebrating Matt Ritchie's stoppage-time equaliser which rescued a 2-2 draw for Newcastle.
Trouble caused by supporters entering the field of play has been in the spotlight following a series of high-profile incidents last weekend.
Birmingham supporter Paul Mitchell was jailed after punching Aston Villa midfielder Jack Grealish in last Sunday's second city derby, while a man has been charged with common assault and invading the pitch during the Premier League game between Arsenal and Manchester United.
Those events followed Rangers captain James Tavernier being confronted by a pitch invader at Hibernian two days earlier.