The 35-year-old defender has endured an injury-plagued season but played the full 90 minutes and netted the third goal in the emphatic, if not always totally convincing, triumph which lifted Barca to within a point of Primera Division leaders Real Madrid.
Pautasso, speaking to the press in place of head coach Gerardo Martino, said on www.fcbarcelona.com: "Puyol has a lot of playing time left. He has a lot of authority.
"Every time he plays he gives us answers. He's always there to help the team and he's an example for us all."
After Real and city rivals Atletico Madrid had played out a 2-2 draw earlier in the day, Sunday's late contest afforded Barcelona the chance to get right back in the title mix after last weekend's costly defeat at Real Sociedad.
Alexis Sanchez set the hosts on their way in the 10th minute before a superb Lionel Messi free-kick made it 2-0 inside 25 minutes.
A moment's sloppiness in the Barca back line allowed Angel Trujillo to pull one back for Almeria and at 2-1 Barca endured more than one or two nervy moments as the visitors probed for a leveller.
It took until the 83rd minute for Barcelona to finally put the contest to bed, Puyol following up with a smart finish after Messi's header had come back off the bar, and there was still time for Xavi to also get on the scoresheet with a sumptuous fourth.
Pautasso felt the scoreline was fully merited.
"The first half was impeccable," he said. "We constantly created chances, and we did well to recover possession.
"We had 10 clear chances to score, but in the second half we lacked depth, despite having the ball.
"In the end, however, we closed out the game. The goal margin we won by is justified."
He added: "We created great goalscoring chances but we still need to capitalise on them. The most important thing is that we managed to create chances."
Midfielder Sergio Busquets was delighted to have got back to winning ways after the Sociedad setback, but acknowledged there was room for improvement.
"The players were eager to play and win again," he said. "It wasn't our best match, but it was important to win the three points.
"(The Madrid derby draw) was the best result for us and we took advantage of it.
"We didn't have that certain spark in our play, but we're content with our performance.
"We have to try not to concede goals from set-pieces, but we aren't a very tall team so we know that this can happen."
Pautasso said the champions would indeed be working on dealing better with set-plays.
"We are a short team and that makes aerial plays difficult for us," he said. "In some situations we use a zone marking system, in other we mark man to man - our rivals take advantage when they get set-pieces.
"We will try to improve in this regard and we will try to avoid conceding risky free-kicks and corners."