Vilanova is to step up from assistant to take the reins at Camp Nou next season after Guardiola announced on Friday he would not be continuing beyond the end of the current campaign.
After an astonishing four-year reign, during which he led Barca to 13 titles, including two Champions League triumphs, Guardiola said he needed to take time out to recharge his batteries.
"We all wanted Pep to continue," Barca's shaggy-haired defender Puyol told a news conference on Saturday.
"Once he had decided to go for the reasons he gave, which we understand and respect, the best news we could have had was that Tito Vilanova would be staying.
"It's a blow Guardiola is going, but Tito staying means the project continues. Tito knows the team better than anyone, knows a great deal about football, and understands the philosophy perfectly.
"He is the ideal person to continue the project."
"We hadn't picked it up at all, a week ago I would have bet everything on Pep continuing," Puyol said.
"We have to thank Pep for everything he has given us. He marks a before and an after in football."
However, they still have the King's Cup final against Athletic Bilbao, who they beat to lift the trophy in 2009, which offers the chance for a 14th title of the Guardiola era before he leaves.
"You are always motivated to win a title," Puyol added, "but now what we want to do, is to win it for him."
