Both struggled with the bat as Salt made just nine and Rashid a duck as the Strikers were bowled out for 135 by Sydney Sixers.
However, Rashid helped the Strikers fight back as he took 4-22, including his third T20 hat-trick, dismissing James Vince, Jack Edwards and Jordan Silk across two overs. Despite the stunning spell from the Afghan leg-spinner, the Strikers lost by two wickets.
The Strikers were able to bounce back later in the week when they took on the struggling Melbourne Renegades.
Salt and Rashid were joined by Sussex team-mate Travis Head in the matchday XI for his first Big Bash appearance of the season following his success with the Australian Test side against New Zealand.
Batting first, Salt made 18, skipper Head 22 and Rashid 2 not out in a total of 173/6 before the Renegades were dismissed for just 110, with Head (2-26) and Rashid (2-19) starring with the ball.
Meanwhile, Chris Jordan had a decent week with his side, Perth Scorchers.
Despite Jordan being wicketless in his first game of the week versus opponents Melbourne Renegades as they racked up 175/5, the Scorchers were still able to run out comfortable winners, winning by six wickets to close the gap to the top four.
The Scorchers continued their winning run, beating Brisbane Heat by 34 runs with Jordan taking figures of 2-44.
Ravi Bopara had a mixed week with his Bangladeshi Premier League side, Rajshahi Royals. He made just four runs in the Royals total of 166/8 as his side were beaten by seven wickets by Chattogram Challengers.
The Royals bounced back later in the week, taking on Chattogram Challengers again but this time winning by eight wickets, Bopara not batting on this occasion.