The Tigers had looked on course to banish the memory of their three-match losing run with a win after goals from Jarrod Bowen and Nouha Dicko overhauled out David McGoldrick’s sixth-minute opener.
But, after home goalkeeper Allan McGregor saved a penalty from McGoldrick in the second period, Spence poked home in the 88th minute to earn the visitors a share of the spoils.
Despite the disappointment of conceding late on, Slutsky was pleased with the improvement he saw in his side’s performance.
“Last time out we had a lot of problems – I had a very difficult time,” the Russian said.
“(Saturday) we again didn’t win, but I think – in terms of performance – we played our best match for the last three matches, absolutely.
“In the last two matches against Middlesbrough and against Sheffield United we played really terribly and I thought about how it was possible to change the quality of the game, change the performance because I can’t change results.
“We conceded the first goal and I was really afraid in this situation because in the last matches when we conceded a goal we stopped playing.
“And (against Ipswich) we played really well, we changed the match and scored twice, we controlled the game and dominated in the game.
“Of course we’re very disappointed with the final result, but we’ve had a lot of negative moments – especially last time – and we’re building a new team.
“We were born only three months ago so we are a small child now.
“And for us, it was a step forward because we showed a really good performance.
“Of course I understand our supporters are very disappointed with the result, but I think everybody understands we tried to play for our supporters and we tried to show our maximum level.”
Ipswich manager Mick McCarthy was happy to leave with a point, which he felt his side thoroughly deserved.
He said: “It was a valuable point, a well-earned point, I thought. I don’t think we’ve nicked anything by any stretch of the imagination. I thought we started well and I thought we let them off the hook in the first 20 minutes and then they got into it.
“My lads kept going, which was great, and I think we got the point we deserved, to be quite honest.”
Hull City: McGregor, Tomori, Dawson, Hector, Aina, Stewart, Larsson (Meyler 81), Bowen, Henriksen, Grosicki (Irvine 68), Dicko (Diomande 89). Unused substitutes: Mazuch, Marshall, Evandro, Clark.
Ipswich Town: Bialkowski, Spence, Chambers, Webster, Knudsen, Skuse, Connolly (Bru 80), Garner, Waghorn (Ward 80), Celina, McGoldrick (Sears 86). Unused substitutes: Gerken, Iorfa, Nydam, Kenlock.
Referee: David Coote (Notts).