Two goals from Katey Turner turned the game around after Forfar had taken the lead through Nicola Davidson.
Murphy expressed his views on how important it was for Rangers to pick themselves up after the defeat against Hearts.
He said: “It was vital to get three points today. Obviously we were so disappointed from last week’s performance, as well as the defeat but it was more so the performance.
“I thought today that, although it was 2-1, for the majority of the game we dominated.
“Credit to Forfar they were well organised, they looked to go play football in the right fashion which is always good to see.
“We really had to grind out this result today and that’s what pleased me most. The determination and grit that the players showed and the desire to go and win the football match.”
Murphy gave individual praise to youngster Claire Adams who was picked out as player of the match for the home side.
He said: “I thought she was the best player on the pitch. She was so composed in possession, her decision making of when to pass and when to drive with the ball was excellent. Her positional awareness and discipline was great as well.
“One thing I would say is that we don’t want to put too much pressure on her, she is still young and she still has a lot to learn and add to her game but today she made a massive contribution to the game.”
A turning point in the match was the introduction of Lisa Swanson which allowed Rangers to switch formations and have two upfront pressing the Forfar defence and Murphy confirmed this was exactly what he wanted.
He said: “A win was everything for us today, I spoke to the rest of the coaching staff about what we’d do if it were goalless with 20 minutes to go and we already planned to play 3-4-2
“When they went the goal up it made our decision easier and we implemented it quicker. We got Lisa on and the two upfront gave Forfar a few more problems to deal with.
“They held the ball up well and had support from midfield and it turned the game for us and led to us getting the two goals.”
Murphy was visibly elated with both Rangers’ goals as he gave an animated touchline performance and he admitted that he felt the need to play his part.
He said: “Most people who know me, know I’m quite reserved on the touchline but I felt that after last week’s performance and having been down to ten the majority of the game, I had to be on the pitch with the players today.
“I suppose that’s probably why I was more animated today, I wanted to get every ounce of energy out of those players, I wanted to play my part, rather than just sit in a dugout, I wanted the players to know I was out there with them.”