The home side made a lightning-quick start and went ahead on two minutes through Matty Tymon but Town fought back and levelled through Luis Adlard on 34 minutes.
United restored their lead three minutes later through Jason Kennedy but Agnew was angered by a foul on him in the build-up to the goal.
He said: “It was a clear foul on me by their lad as he had hold of me with both hands, then he headed it across goal for their lad to score.
“We gave it a good go against the best side in the league, Liversedge may be top but Marske play the better football.
“In the second half we had enough chances to at least draw and maybe win the game.
“At the end their supporters and coaches were saying that they - Marske - had been lucky to win it and to be clapped off by their fans at the end shows how well we did.
“Their winning goal should have been chalked off and it is annoying as the same thing happened in the 1-0 loss at home to Worksop on Saturday.
“No-one expects us to get anything from these kind of games but on saturday it had 0-0 draw written all over it as both keepers were very strong on the day, but when you are having a bad run the rub of the green does not go in your favour.”
“But we cannot dwell on that, we need to get back to it Saturday when we have another very tough home game against leaders Liversedge.”
Flynn McNaughton has left the club due to work commitments, signing for relegation rivals Pickering, but the Seasiders will be boosted by the return from suspension of Nathan Hotte on Saturday, while Danny Earl - who cannot play midweek matches due to work, will also be back.
The Seasiders have also signed youngster Blake Drury from Selby Town.
Agnew added: “Blake is a left-back or left wing-back and will give us some good cover on that side of the pitch.
“He did not get chance to come on against Marske as it was a proper battle and hard to bring someone on into that.
“I am also hopeful that we can another player in before Saturday’s game.”
Town face a home game against Sculcoates Amateurs in the East Riding FA Senior Cup quarter-finals on Tuesday night, 7.45pm ko, and Agnew is keen to get a win in the cup-tie.
He said: “I want to win that competition so we need to be ready for that game.
“We have had a poor run recently but we need to get back to winning ways and start picking up some points and a win in the cup can give us momentum.”