“Our deepest sympathies and solidarity to the British people, the victims and families of the #Manchester attack”, Costa said in a message in English on his Twitter account, following a similar message in Portuguese.
Meanwhile, Portuguese officials have said that there was no indication that any citizen of the country is among the victims of the bomb attack on Monday night outside the pop concert in Manchester.
The Ministry of Foreign Affairs has been monitoring the situation since news broke, given that there are hundreds of thousands of Portuguese living in the UK.
A Portuguese dad who was at the concert with his young daughter and who escaped uninjured told newspaper Correio da Manhã of the terror they experienced that night.
Fabio Silva, 34, who emigrated to Manchester, said: “It was all going well and when we were leaving we heard a big bang and I did not realise what was happening.”
He elaborated that, at the end of the concert, when he was in the corridor to the exit, he heard a rumble and “at that same moment everyone began running and screaming and crying.”
On Tuesday, the commander of Greater Manchester police, Ian Hopkins, announced an increased death tally of 22, which rose from an initial 19 fatalities, adding that 59 people are being treated in eight different hospitals in the region.
He said that police believe one man only was involved in the attack, and that he was carrying an improvised explosive device that he himself detonated. He is believed to have died in the explosion.
The attack took place in the foyer of the venue where US pop singer Ariana Grande was performing, who has a fan base of teenagers and children.
So-called Islamic State has since claimed responsibility for the attack.
In the meantime it has yet to be seen whether the pop star will continue her tour after she temporarily suspended it following the Manchester bombing.
Grande is due to perform in Lisbon on 11 June as part of her current world tour and it would be her first concert in Portugal.
Portuguese promoter, Álvaro Covões, told Lusa News Agency on Tuesday that so far there was no indication of the American singer’s concert in Portugal being cancelled.
Lamenting the “absurd terrorism” rocking the world at present, he declined to confirm whether security would be upped at events in Portugal citing professional reasons.
“Security should not be discussed in the public arena. At most major events, the public will have felt a strong security presence and there are always emergency plans approved by the authorities.”