Goals from Maxi Rodriguez, Dirk Kuyt and Luis Suarez secured a comfortable victory for the hosts at Anfield
The hosts finished as comfortable winners after an early Maxi Rodriguez goal was built upon through a second half Dirk Kuyt penalty and a Luis Suarez strike and the Scot believes that his side deserved its win.
"It was a difficult day for both sets of players," he told reporters, "it was really hot for them and after we took the lead they put us under a bit of pressure through set plays and crosses but in the second half we loosened up a little bit, got two goals and I think we deserved to win.
"I didn't expect to get a stroll in the sunshine, they've been playing well of late. They got a good draw at home to Man United and maybe the Andy Carroll factor added a wee bit of spice for them but as I say, it was a tough game but I think we were deserving winners.
"Some of the passing and movement has been better than what it was today but their determination and effort was the same has it has always been."
Dalglish replaced Maxi on the 70 minutes with Andy Carroll, who made his first appearance against his former club since moving to Anfield in January for £35 million having been recently sidelined through injury.
Speaking of the decision to bring on the striker, the Reds boss said: "We never made our mind up until we knew he was fit. If he wasn't fit, he wouldn't have got any minutes. He's only had two days training so it was best for us to start with other people. He's here for five years so he'll have plenty of opportunities to play.
"I think when he goes to St. James' next year he'll get it again from the Newcastle fans. He's a young boy but he's got broad shoulders."
The Scot also praised youngster John Flanagan who performed manfully against a tricky customer in Jonas Gutierrez and claimed that the full-back handled both the Argentinean and Joey Barton well, having switched from right to left at half time.
He said: "I think he won the the test against Gutierrez and against Barton. He made the first goal and then he's been moved over and it worked out well for us.
"Flanagan has done brilliantly, he has surpassed all of our expectations and it's great credit to him. He got booked but he kept trying and kept playing and he's been a great credit for us."
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