Peter Houston and Barry Smith have called for Calum Murray to rescind his decision to send off Johnny Russell and Stephen O'Donnell in yesterday's Dundee derby.

The two players were dismissed in the second half at Tannadice after colliding on the ground and pushing each other.

The Dundee United and Dundee managers both felt the decision was harsh. Murray could, though, claim it was justified, since Russell used his leg to nudge away O'Donnell, while the Dundee midfielder use a clenched hand. Yet there was little aggression in their actions.

"I don't think either are sending-offs," Smith said. "The referee will have a look at it and realise it was just a coming together and hopefully both are rescinded. If the referee sees that he's made a mistake, we won't have to appeal it. Hopefully he'll see he made the decision too quickly, but in the heat of the moment it's understandable."

Houston agreed that the referee ought to think again about his decision when he reviews it. The Dundee United manager watched the incident afterwards, with television coverage providing several views of the players' tangle, and he felt that Russell, in particular, was treated harshly. "At best for the boy O'Donnell it was a yellow card, but Johnny did nothing," Houston said. "The boy's come in and caught Johnny – not badly, it was a foul, they tangled – but Johnny didn't lash out, so I'm wondering what he did. [If required] I'll speak to the chairman and try to get him to spend £1000 on appealing it."

The 3-0 victory was United's second consecutive win by that scoreline at Tannadice. The clean sheet was just as pleasing as the goals to the manager, but while fans will revel in a victory earned despite the team not playing at its best, Houston will recognise that was, in part, due to the mistakes made by their opponents.

He refuses, also, to set targets beyond reaching the top six, with United's squad still short of strength in depth. "I expected us to play better in the second half, we were sloppy and got caught up in things," he said. "It's hard to be critical, although the boys were moaning with one other at half-time. You can play brilliantly in derbies and not win them, so the most important thing was getting the three points. But when we sit down to watch it again, we'll know we can play a lot better.

"Aberdeen and Hibs have bigger budgets than us. Top six is achievable, but I wouldn't look beyond that at the moment. If I get two or three injuries or suspensions, it's very young kids I'm having to bring in who are untested. I really need another couple of players, but we have to be realistic that the club can't get me any more money. We have a good 15, 16 players but you're going to get players who have a dip in form or get injured."

Smith was frustrated with his team's performance, and the recurring mistakes that have made their return to the top flight a chastening experience so far. They should have opened the scoring, but ended up conceding from a set-piece then two counter-attacks.

"We're conceding goals at this level that you can't afford to do," he said. "We need to show more spirit. There was an incredible following from the fans and sometimes the players should look to see what it means to play for this club."