The Brazilian finalised the transfer on Monday after the two parties agreed on a reported £142m fee.
The 25-year-old was coveted by the Spanish giants in the summer, but Liverpool held firm and knocked back their offers, which were rumoured to have surpassed £100m.
Barcelona did not give up, though, and they finally got their man when the transfer window reopened this month.
"I'm still digesting it as a Liverpool fan," Gerrard told BT Sport. "Yeah [I feel a bit sick]. I'm not surprised by [the move]. I know Liverpool have done everything they can to keep him and they fought very hard to keep him until the summer.
"But when a kid's got a dream, a South American, that he wants to play for Barcelona and he thinks this is the only opportunity he's going to get, then it's very difficult to stop it.
"There's no doubt about it, Liverpool will miss him. He's a wonderful footballer, a great person and to be fair to him he hasn't downed tools at all. I respect his decision and wish him all the best. But Liverpool will go on. They've got big money for him and I'm sure they'll replace him with the right people."
Coutinho will not make his debut for another three months as he nurses a thigh strain.