The Tigers brought a run of four straight defeats to an end by securing the point at Goodison Park, courtesy of substitute Sone Aluko's 59th-minute equaliser, which took them out of the Barclays Premier League relegation zone.
And Bruce, whose side had trailed to Romelu Lukaku's 34th-minute strike, said afterwards: "We needed a result and to give everyone a lift because it has been difficult over the last month.
"I have learned that this league is unforgiving and you can quite easily go four games without picking up anything.
"It was always going to be difficult, especially when we went behind, but thankfully we have taken something from the game, and with Nikica Jelavic's header (that went wide just after Aluko's goal), we were close to winning it.
"For me, if there was going to be a team that won it, it was going to be us in the second half."
Bruce made four changes to his first XI from the 3-0 loss at Manchester United on Saturday, and he added: "I don't think I've really played the team which, in my mind, is my best team, for one reason or another.
"But I'm still convinced we have a squad that will improve us from last year, because we have more depth - and that showed tonight."
Hull, up a place from 18th to 17th and separated from the relegation zone on goal difference alone, finished 16th last season in their comeback top-flight campaign and also reached the FA Cup final.
Bruce is convinced he has a better group of players at his disposal this time around, despite their disappointing start to 2014-15.
"We don't like to be in the bottom three," he said
" The one thing we managed last year was beating the teams I thought would be around us
"The Premier League already has a familiar look - the bottom eight or nine teams you would expect to be there, and our aim is to be at the top of that group if we can.
"We are under no illusions how difficult it will be - it is our second season, and sometimes that is harder than the first.
"There is no expectation first time around
Nobody gave us a hope in hell of staying up last year and we managed to do it easily.
"This time no one thinks we are going to get relegated, and that is the expectation we have to deal with.
"But from what I have seen tonight and all season, we will be okay
I'm convinced."
Everton were in control in the first half but could not make the most of it, with one goal ultimately proving not enough.
They struggled to get much going after Aluko got past Sylvain Distin and beat Tim Howard at his near post, and had faded badly by the final whistle.
Everton boss Roberto Martinez, whose side stay 11th and are now seven points off the top four, suggested Hull had employed time-wasting tactics.
He said: "I'm not pointing the finger at them, but I do think Hull were stopping the clock and making it difficult to get momentum.
"I thought the referee rightly awarded an extra six minutes (of stoppage time).
"I'm not bitter about the way the opposition played - that is their choice
The disappointment is that the first-half performance was good enough for three points."
There were some boos from Everton fans as the players went off at the end.
And Martinez said: "I think it was a reaction at having three points in the bag, and having the feeling that the first-half performance had been dominant enough to win the game, and then all of a sudden, you end up with one point.
"At the end we couldn't find the energy to have a final push.
"Expectations are high and it was more of an emotion today than a moan, the way I see it."
Source : PA
Source: PA