The Toffees twice came from behind to lead 3-2 with a couple of minutes remaining only for Daniel Sturridge to salvage a point with a late header.
Prior to that Reds goalkeeper Simon Mignolet had been much busier than his counterpart, denying Romelu Lukaku three times before his two goals and also Gerard Deulofeu.
"Mignolet was brilliant. We need to be more composed and clever in front of goal because four or five times we worked ourselves into positions which are difficult to get into and when we do that we need to take advantage," said the United States international.
"We are disappointed in the way we conceded the goals (all from set-pieces) but that can happen.
"It is not something we are proud of - the fact we gave away three goals, especially at set-pieces.
"There were small mistakes that got punished but they will be corrected.
"We played really good football. We dominated the game, they hit us on the counter-attack, but for the most we controlled a lot of it and created a ton of chances.
"In the end it's two points dropped but it was a good derby."
The only downside to a thrilling game was injury to left-back Leighton Baines, who was forced off just after half-time with a toe injury on his right foot.
Everton are awaiting the results of x-rays to assess the damage and Howard is hoping it is not too bad.
"Fingers crossed for sure it's nothing too serious because we need him," he told evertontv.
Manager Roberto Martinez, who became a father for the first time on the eve of the game, enjoyed his first Merseyside derby experience if not the result.
"This is one of the best environments I've seen where football can be seen," said the Spaniard.
"In terms of the football we had a bit of everything but we were pretty disappointed to concede three goals from dead-ball situations.
"I thought the first half, without being at our best, Liverpool did not have a shot on target from open play and they got two goals.
"That was a really hard blow to take because at half-time it put us in a really difficult position.
"We had to risk it, we had to gamble and open the game and make it box-to-box and we were magnificent in terms of the number of chances we created.
"I thought to get the third goal and be ahead was down to an outstanding performance from the players."
Lukaku claimed the plaudits with two second-half goals but in truth he had not offered much of a threat up to that point.
Liverpool had taken a fifth-minute lead when poor marking at a corner allowed Philippe Coutinho to fire home but within three minutes the Toffees were level when Kevin Mirallas equalised.
A brilliant Luis Suarez free-kick restored the visitors' lead before the real moment of controversy came when Mirallas' knee-high challenge on the Uruguay international resulted in only a yellow card.
That Mirallas went on to have a hand in his compatriot's two goals after the interval only rubbed salt into the wound but Sturridge, coming off the bench, denied Everton victory late on.
"I think it would be unfair to highlight one player. I thought both sets of players were sensational," was Martinez's assessment.
"I thought Romelu was really clinical in front of goal and Gerard Deulofeu, when he came on, looked ready to excite fans in the Premier League.
"Ross Barkley performed in a very mature manner and was a joy to watch and overall I thought the young players adapted really well under the guidance of the senior figures."