The young English midfielder saw red for a first-half challenge on Luis Suarez, which replays showed to be a harsh decision by referee Martin Atkinson, and will no doubt be seen as a turning point as Everton went to concede second-half goals from Suarez and Andy Carroll.
Speaking after the game, Dalglish told Sky Sports: “Up until the sending off I feel it had been an even game. Luis Suarez had a chance for us, and then I think Cahill had a good header up the other end and Pepe Reina made a great save and there wasn't much between the teams.
“Obviously sometimes the numerical advantage works in your favour, on other occasions it can work against you.
“They’ll be disappointed to have lost the game but I don't think David Moyes can be disappointed with the attitude and effort his team put in.
“It was difficult, it was hot out there and we kept moving the ball around well and kept our patience so I think we are delighted with the result
“Whether we'd have won or not if they hadn't gone down to 10 men I don't know.
“I haven't seen the sending off - I don't intend to watch it either, I just want to enjoy the next two weeks now.
“We were very professional in the match. When you are against 10 men it is easy to lose your concentration and get complacent but we didn't do either of those two things.”
As well as the advantage handed to his side, the Scottish manager believes his team put in a good performance in order to ensure the victory and the players will take a lot from the win.
“Everyone has done well for us today," he added.
“Andy Carroll has got himself off the mark now with league goals which is great for us. Dirk Kuyt missed a penalty but it didn't affect him and he kept working away which is great credit to him and then Luis Suarez gets another goal so it's a good result for us.”