The Vatreni were 2-1 down to Les Bleus and pushing for an equalizer in Sunday's game when four individuals dressed as security personnel took to the field and forced a halt in play.
One of the invaders attempted to give Lovren a high-five but instead found himself thrown to the floor by the Liverpool centre-back as all four were eventually removed by stewards.
"I really was mad because we'd been playing at that moment in good shape," the 29-year-old, whose side lost the final 4-2, is quoted by the Daily Mail as saying.
"We had been playing good football and then some interruption came. I just lost my head and I grabbed the guy and I wished I could throw him away from the stadium."
The four individuals have been jailed for 15 days by a Moscow court for their actions.