Clint Dempsey rose highest to nod home Damien Duff's corner in the 82nd minute - the United States international's 16th league goal of the season - to cancel out Frank Lampard's controversial 45th minute penalty.
"I thought we were good value," Murphy told Sky Sports 1.
"At one point I thought we looked like the team going to win it. In the first half we played good stuff and felt a bit aggrieved to go 1-0 down.
"I haven't seen the penalty back but the referee tells me there was a touch behind as he come into me with the tackle and he gave it. It was a good penalty from Lamps, as usual.
"But we did feel disappointed and that showed in the first 10 minutes of the second half. We were a bit flat but got a grip on game. I thought possession-wise we were as good as them if not better.
"We've played some great stuff at the Cottage. Even though it's only a draw, that's one of our best performances this season, I think."