The Toffees moved above Liverpool thanks to goals from Leon Osman and Victor Anichebe but Hodgson believed the game would have taken a different turn had Chris Brunt not fired his effort wide off team-mate Shane Long.
“We missed a cutting edge. We went behind unfortunately with the deflected goal but were playing quite well up to half-time and could have had an equaliser,” he said.
“It was going to be very important to keep that going in the second half but the second goal killed that off.
“It gave Everton the confidence they needed to keep the ball and punish us on the counter-attack.
“In the end we were thankful to some very good defending from Jonas Olsson and the goalkeeper (Ben Foster) to keep it to two.”
England manager Gareth Southgate has claimed that the country needs to boot racism out of its own football before criticising World Cup hosts Russia.
Newcastle have been linked with a shock move for former Sunderland goalkeeper Simon Mignolet during the summer.