The problem here is the fans rather than the manager - small minded, short termist couch potatoes who will get stuck in at the first sign of of bad run, compounding the negativity, when actually what the team, and manager needs to get out of this situation is some strong support.....
One of the best strikers we've had statistically has been Romelu Lukaku - underappreciated and criticised by the fan base - who then wonder why he rubbed in his goal celebration on his return
Martinez deserved the criticism in the end and was kept in a year too long - he'd been given plenty of time however. Koeman hasn't had time yet - lots of change in the team and a tough fixture list which isn't getting any easier - Lyon, Arsenal, Chelsea coming up....
Who would you replace him with? David Unsworth? (with respect, total gulf in terms of experience). It was hard enough to get him in and a replacement of the same callibre would be hard to come by. People wanted Lukaku out and then discover how hard it is to attract and land a quality replacement
The best thing fans can do is support Koeman and the team - provide the positivity to help turn results around. Buying a striker and center back in Jan will help the cause...