Cotter will leave the Scotland job and be replaced by Glasgow boss Gregor Townsend at the end of the season.
Strauss, who will start at number eight against Ireland on Saturday, says the Scotland players want to send Cotter out on a high.
"When people move on you want to give them a good send off," Strauss said.
"It does bring that little bit more of an incentive. You do try that little bit harder. You need emotion to play rugby and it does give you that little extra edge."
Scotland have not won an opening day Six Nations fixture since the victory over France at Murrayfield in 2006. Their record against Ireland in the championship does not offer much cause for optimism either. Ireland have won 14 of 17 Six Nations matches between the sides.
Moreover, Joe Schmidt's side have beaten South Africa, Australia and New Zealand since last summer, with Munster's CJ Stander a stand-out performer, and a player with whom Strauss is well acquainted.
"We shared a room at the Springbok camp for a week back in the day," Strauss said.
"He's a farmer from up north in South Africa and I'm more of a beach boy from down in the city in Cape Town. We get along well and he's a very nice guy.
"He's a very tough player. Even with the Bulls, I played for the Lions so there was a very big rivalry between our two South African teams. He was always one of the guys we watched out for. He's come over and he's done exceptionally well."
Scotland resource coach Nathan Hines, who will follow Cotter to Montpellier in the summer, warned that Schmidt will have pinpointed every Scottish weakness ahead of the Murrayfield clash.
"He brings an unbelievable tactical awareness," said Hines, who played under Schmidt at Leinster.
"He goes through the other team with a fine-tooth comb and finds their weaknesses. That gives his teams confidence.
"I was across at the end of last year and spoke to him. The door is never closed with Joe, unless it is and he hasn't told me yet! He's an open guy and we had some good times with Leinster so I'm sure he'll give me a cheeky smile on Saturday before kick-off.
"They're very good at what they do. They find weaknesses and they exploit those weaknesses and make it very hard for you to play. It's about how we combat that and how we make it as difficult as possible for them to execute."
Ireland captain and hooker Rory Best expects to wage a punishing set-piece battle with Scotland's inexperienced front-row.
Edinburgh's Allan Dell, and Glasgow duo Fraser Brown and Zander Fagerson have just nine Test starts between them (three each), but 100-cap Best warns their lack of international appearances will not make for an easy ride.
"When you get that two-three link that play together every week, train together every day, it helps a lot," he said. "There's no doubt that will play into their hands.
"They're inexperienced if you look in terms of Test rugby as a combination but if you look at what they've achieved individually so far this season….to go to Welford Road and dominate the way Glasgow did and the way they've been performing, we've played against them provincially and it's a very tough task scrumming down against that Glasgow scrum.
"They form two-thirds of the front row on Saturday. We're under no illusions that it's going to be a tough ask. They're quality players."
Josh Strauss believes Vern Cotter's impending departure will provide added motivation for Scotland to have a successful Six Nations.