Drogba managed to waste a crucial six-and-a-half minutes in the Blues' 1-0 win in Wednesday's night's semi-final first leg after collapsing to the ground several times in apparent agony. Barca initially reacted by sportingly kicking the ball out of play but eventually became infuriated by Drogba's antics, with captain Carles Puyol letting rip at the 34-year-old.
A diplomatic Pique, who could be charged with marking Drogba in the second leg, said: "I believe in Drogba that, every time he fell down, it was because he was in pain, or he felt a kick on him. I don't think that, when Drogba fell down, he was trying to act or dive."
He added: "If not, we'll start to talk about football not having fair play and being all about cheats. Football is not like that.
"We have to keep all the good things, and diving and cheating is not good. If he keeps doing that, you might end up thinking that's the case (that he is not hurt). But I believe in his honesty."
Despite his theatrics, Drogba was outstanding on Wednesday night, scoring the winner and proving a handful for Barca's defence. Pique, who has missed the world and European champions' last five matches, could be recalled specifically to combat the striker.
The 25-year-old's only experience of playing against Drogba came in the 2009 Champions League semi-final and he revealed he was considering consulting former United team-mate Rio Ferdinand about dealing with the Ivory Coast star.
"Rio sent me a text message and wanted to talk to me today," he said.
"Maybe that's what he wants to talk about. We could talk about Drogba. He's one of the best forwards I've ever seen. It'll be a very hard duel if I'm in the starting XI."
Pique has also played down reports of a rift with Pep Guardiola, saying he believed he was left out of the Spanish and European champions' last two matches for purely sporting reasons.
The Spain centre-back was an unused substitute in the first leg defeat at Chelsea last week and Saturday's reverse in the La Liga Clasico at home to Real Madrid, prompting further speculation his relationship with Guardiola had broken down.
Pique said he was focusing on working hard to win back his place in the starting XI.
"This is a new situation for me because I am used to playing and I haven't had a chance in the last couple of matches," Pique told a news conference on Monday.
"But it's a technical decision for the manager and he chooses who plays and you have to respect that," added the former Manchester United player.
"Every year there are new players and he chooses the team he thinks most capable of winning.
"I take each match at a time and train hard and try to show the coach I deserve to be in the team."
Pique has been a key player for Guardiola since the former Barca and Spain midfielder took charge in 2008, helping the club to 13 trophies including three successive Spanish league crowns and two continental titles.
Spanish media reports have suggested Guardiola does not approve of the high-profile lifestyle Pique leads with his pop-star girlfriend Shakira and even that the coach has asked the club to sell the player as a condition for extending his own contract beyond the end of this season.
"We arrived here together the same year, him as coach and me as a player," said Pique, who came through Barca's youth ranks with Lionel Messi and Cesc Fabregas before moving to United.
"We are part of a very important era for this club and I really trust him," he added.
"I think he (Guardiola) will stay as he loves this club and this team.
"Our relationship is very, very good and we talk much more than you might think. Our daily contact and our daily discussions are very positive.
"We don't just talk about football, we talk about everything. He is always tough on me but I like that."
Guardiola said it was not his job to control what players did away from the pitch and that Pique's lifestyle was a fundamental part of his character.
"Gerard has a very full life as a person and I am not going to change it," he told a separate news conference.
"Some players only have football and he has football and many other things and that's very important," he added.
"He is forced to live the way he does because that's his character. I love him as he is."