Brendan Rodgers suffered “the longest 90 minutes” of his career as Celtic survived a scare to reach the Champions League group stage.
The Hoops were heavy favourites to see out the play-off second leg after their 5-2 victory at Parkhead last week but were on the ropes from the early stages at the Turner Stadium.
Scotland goalkeeper Craig Gordon saved a penalty in the 15th minute from Maharan Radi, but the relief was only temporary as substitute Ben Sahar soon headed the Israeli champions ahead.
The visitors conceded a second goal in the 48th minute when a mix-up between Saidy Janko and Gordon allowed Romania international Ovidiu Hoban the easiest of chances to make it 2-0, but the Scottish champions held on.
Celtic boss Rodgers, who declared himself “immensely proud”, said: “It was probably the longest 90 minutes I have faced as a coach, and I think with past experiences that players have had, sometimes they know how it can map out.
“I thought Hapoel Be’er Sheva were outstanding. They had to force the game, of course. They had nothing to lose, but they played very well.
“But I have to congratulate my players, because all the work we have been doing has been based around that mentality and quality of game.
“We know we can’t always play well. A lot of games we have played well.
“But (this match) was purely about resilience and persistence and it was an amazing effort by the players on the back of everything they have been through before.
“So huge applause to them and I delighted they get their rewards after a long pre-season.”
Rodgers believes his players took “a huge step and got their rewards” and will be all the better for coming through such a nervy and fraught experience.
He said: “Tonight they added an extra percent to their mentality.
“I think deep down that maybe they didn’t think they could achieve because of the short period of time we have been working with them.
“But we have built into them a belief that if you work hard and with an intensity that will give you confidence and you give yourself a better chance of winning and when you are stuck you can dig it out.
“Maybe the focus of the criticism when I came in was we couldn’t tough it out but we showed after two games and under a huge amount of pressure that this team could tough it out.
“You can never say you are calm. You could probably see the bench working tirelessly to plug gaps, the players were on auto-pilot towards the end but I thought that towards the end they had just about run out of ideas.
“I think they coped really well but you could never switch off until the final whistle goes.
“It is incredible moment for the supporters, they are going to be back in amongst the Europe’s elite and it is where Celtic belong.”
Rodgers insist there was no surprise that his side rode their luck at times.
The former Liverpool boss said: “We felt that was going to be the case.
“We had to work so hard to shift momentum and block spaces.
“It was a problem for us because we couldn’t keep the ball.
“Eventually we went to a back five in order to try to block out the sides of the field, keep a diamond with one up front with Moussa Dembele coming on.
“That seemed to settle us in the last 15 to 20 minutes and we got some control then.”