Sampaoli's team reached the final with a 2-1 win over Peru on Monday and will meet the winners of Tuesday's semi-final between favourites Argentina and Paraguay at the national stadium on Saturday.
“When Alexis is not in the fullness (of form) that he has us used to, Chile feel it,” Sampaoli said.
“If he is feeling good, he's the most decisive player in this team. We must recover him well because he's vital to us,” added the Argentine.
Sanchez has shown flashes of his class in the tournament but contributed only one of Chile's 13 goals in five matches.
Sampaoli suggested the pressure from home fans to reach the final as hosts and win the 99-year-old tournament for the first time affected the team.
Chile were not at their best trying to break down a Peru side reduced to 10 men for 70 minutes after a red card for defender Carlos Zambrano, he said.
“This was the match in which we most lost our shape. Defensively the team struggled a lot to get their shape to recover the ball, we usually get it back much quicker than today (Monday),” Sampaoli said.
“Our anxiety played against us,” Sampaoli told reporters.
Defender Mauricio Isla, scorer of the goal that gave Chile a 1-0 win over 2011 champions Uruguay in their quarter-final, echoed that sentiment.
“It wasn't our best match, we had been showing good touch, great finishing and today we got tired,” he said.
“Peru complicated us quite a bit, even with a man less. I think the pressure got to us.”
The Peruvians were not given much of a chance before the tournament but Sampaoli believes they can carry their much improved form into the 2018 World Cup qualifiers starting in October.
“(Peru) grew throughout the tournament and their big names became stronger and are in great form,” said Sampaoli of the work of their coach Ricardo Gareca in the short time he has been in charge.
“From midfield towards the front they have nothing to envy any national team in the Americas.”
Peru had a poor 2014 World Cup qualifying campaign and are still looking to reach the finals for the first time since 1982.
Original source: Chile coach banking on Sanchez