Captain Alastair Cook (22) and Joe Root (2) were both dismissed early during the Three Lions' second innings in Durham, before Ian Bell hit 105 not out to rescue his side and leave the hosts with a lead of 202 at stumps on 234-5.
Apart from Root's 180 at Lord's and three Cook half-centuries, England's opening pair have struggled to survive against the Australia attack, much to the annoyance of Strauss.
"The opening partnership is such an important one for setting the platform for the middle order to come in and play more free and expressive manner," Strauss told Sky Sports News. "Both sides have struggled at the top of the order. We saw Chris Rogers score a good hundred for Australia yesterday but Cook and Root have both had to graft their way through.
"Alastair Cook, meanwhile, has battled hard but his dismissal today was a very uncharacteristic shot from him and shows he's searching for the ball a little bit at the moment."
England resume at the crease on day four with Bell and Tim Bresnan.