"The 90 minutes just confirmed to us what we already knew - that we need to strengthen the squad before the end of August," McClaren told the club's official website.
"The chairman is fully behind us. The backing is there but it is just about the process of getting the players in. The good thing is that we still have time to do that."
The former England head coach added: "A lot of what we did was very good and it wasn't the worst of days because we got a point and kept a clean sheet.
"The workrate and attitude of the players was excellent - I couldn't fault that. But it was plain to see that we need more quality in the final third of the field.
"But I must confess it was one of those opening-day things, sometimes you just get a bit of an anti-climax. We got a big crowd in, there was a lot of expectation and we wanted to do well, but it just didn't quite work out for us.
"We never looked like getting the moment that would have brought the win but we kept going right until the end and that pleased me very much."