The result came on the back of last week's drought-breaking win over the Newcastle Jets and Thursday's announcement of Heart being acquired by English Premier League giant Manchester City.
Van 't Schip felt the demeanour of his charges was a stark contrast to what would have been the case following an away draw against an in-form opponent earlier in the season.
"Seeing the boys disappointed in the dressing room after playing 2-2 against Adelaide, that's a totally different kind of atmosphere than you would have expected a few weeks ago," he said.
"I think it's a very good result looking at Adelaide the last few weeks and where we've come from.
"We had the chance to go away with three points, but looking at the game I think 2-2 is the right result."
Bruce Djite's 22nd-minute strike gave the Reds the early advantage before Heart hit the lead through second-half goals to ex-Leeds United duo Harry Kewell and Patrick Kisnorbo to sniff a rare interstate triumph.
Ryan Griffiths equalised in the dying moments, allowing Adelaide to snatch a draw, but van 't Schip was impressed with the character his team showed in responding to the Reds' initial punch.
"Adelaide made it difficult," the former Dutch international said.
"We started okay but then we lost it a little bit in the midfield.
"Coming back from 1-0 (down) to 2-1 (lead) showed that we have character in the team, after last week (against the Jets) again coming from behind."
Kewell's 61st-minute equaliser came via a penalty after United defender Nigel Boogaard was penalised for his slide tackle deep in the 18-yard box.
Van 't Schip held no concerns about his skipper stepping up and taking the shot after his calamitous penalty miss against Sydney FC last month, now the subject of worldwide YouTube mirth.
"Harry takes his responsibility, not only with the penalty," van 't Schip said.
"He was in the game for 90 minutes, (he was) physical and important to help the team get to 2-1 (lead).
"Mentally he showed character."
In the opening stages Kewell appeared upset by a comment made from the outer.
He immediately gestured for the culprit to be quiet before complaining to referee Kris Griffiths-Jones on the pitch.
Van 't Schip was unsure exactly what was said to Kewell, but the Heart manager admits it is 'sad' that rival supporters regularly afford the Socceroo legend a hostile on-field reception wherever he goes.
"I have no idea (what was said to Kewell)," van 't Schip said.
"I saw something happen but I really don't know.
"Harry should try to focus on the game ... I know it's difficult sometimes.
"It's sad that a player who still means a lot to the game gets treated sometimes in this way.
"It's not only here; it happens everywhere."
