The Magpies were unable to deliver their first home win of the season as Miguel Almirón went close before Steve Bruce's side were fortunate to remain level as Lewis Dunk's deflected header struck the crossbar.
Fabian Schär produced a stunning goal line clearance in the second half and, despite Andy Carroll's anticipated second debut for United along with the return of Allan Saint-Maximin from a hamstring injury, Newcastle were unable to break the deadlock on a frustrating evening on Tyneside.
Hayden told nufc.co.uk: "I think if you asked me after the first half, I would have bitten your hand off for a point but in the second half, we changed our style and, on another day, we could have taken three points.
"We had a great chance in the first half to go ahead and you never know what could have happened after that. That's football for you and it's about taking your chances at the top end of the pitch and if you don't, you're always going to pay for that in dropping points.
"It was frustrating we couldn't get that goal but that's the difference in Premier League football. If you don't take your chances, you can't win any games. Sometimes, with all due respect to other divisions, teams can give you goals whereas you don't really get that too much in the Premier League.
"We need to keep plugging away and try to keep doing the right things. We're trying to do the best we can and know the fans want us to do our best to get as many points as possible. This time last year, we had less points than we currently have so there's progress.
The Magpies travel to Leicester City on Sunday afternoon looking to record their third successive away win at the King Power Stadium but face a Foxes side unbeaten at home since Newcastle's 1-0 triumph in April, with Hayden featuring in the Premier League victory.
"It's going to be a difficult game, like all Premier League games are," the midfielder added. "As a group of lads, we need to stick together. There's going to be difficult periods where we may not win games but we've been here before.
"The last two seasons we've been in similar positions and everyone is demanding of us. We know the club we play for and the pressure there is to play for and we have to stick together like we have done in the last two seasons, which have not ended too badly for us.
"At the back, we have been notoriously solid with our back five in the past couple of years. We've not conceded too many goals, especially at the end of last season, where we were in the top five for most clean sheets. That's hasn't been our problem for us, it's at the other end."
Newcastle were welcomed by he return of Carroll and Saint-Maximin against Albion, with the forwards' entrances from the substitutes' bench rejuvenating the St. James' Park supporters.
And Hayden highlighted the need for current injury absentees to return as quickly as possible to benefit the overall squad.
The 24-year-old added: "It changed the dynamic of the game because with them two coming on, especially Allan and the way he plays and what he brings to the team. It got the crowd off their feet and got them more into the game which helped us push on in the second half.
"We need to get all of these players fully fit because we need it. We need every single player in the squad as we've had a depleted squad at the start of the season with five or six injuries, especially at the top of the pitch. The fitter they can get, the more options we have and we can only be better for it."
