Messi, 30, scored twice and set up a goal for Ousmane Dembele as Barca beat Chelsea 3-0 at the Camp Nouon Wednesday for a 4-1 aggregate triumph.
The double took Messi to 100 Champions League goals while his opener, coming after 129 seconds, was the fastest goal of his illustrious career.
Messi has frequently been linked with a big-money move to the Premier Leaguebut Conte is convinced the striker will retire at Barcelona.
“I think Leo wants to stay until the end of his career with Barcelona,” Conte said.
“We’re talking about an impossible situation. I repeat: we must have great respect for this player. We are talking about a fantastic player.
“I think he wants to stay in Barcelona for the end of his career. I think it’s the right way for him. He’s writing with his team-mates a great story with Barcelona.”
After full-time, Conte left the field with a congratulatory arm around Messi’s shoulder but Chelsea had chances too, most notably through Marcos Alonso and Antonio Rudiger, who both hit the woodwork.
Alonso also thought he should have been awarded a penalty in the second half after he went down under the challenge of Gerard Pique.
Chelsea striker Olivier Giroud believes his team deserved more.
“Obviously on both matches I regret the posts or bars that we could have. You have to have some success, a little luck,” Giroud said.
“What will stick in the throat is the penalty not given where it is quite obvious that Marcos is pushed in the back or he would have at least tried to shoot. It’s very hard, I think it would have changed the game.”
Messi, however, once again proved the difference, applying two clinical finishes through Thibaut Courtois’s legs and, in between, teeing up Dembele to score his first Barcelona goal.
“He knows in certain moments stars have to come out. He forces himself to do that,” Barcelona coach Ernesto Valverde said.
“There’s no guarantee that he’s going to score, but he is a fantastic player. We enjoy him. We’re lucky enough to be seeing something that will go down in history.”
Off the field, however, Barcelona may face questions from UEFA about the treatment of spectators before the game outside the stadium.
Chelsea have invited any fans who experienced problems to contact the club.
A Chelsea spokesman said: “We are aware of reports of incidents outside the ground before the game where a number of Chelsea fans were hurt.
“We ask that our supporters contact us with accounts of their experiences of this evening’s arrival at the stadium so that we can take this up properly with the authorities.”