Warburton, who has signed a one-year extension to his existing deal on improved terms which will run until 2019, also expressed his dismay at criticism of Tavernier and Waghorn in the aftermath of last week’s revelation they have both turned down initial new contract offers from Rangers.
Right-back Tavernier and striker Waghorn, both recruited by Warburton last year, have two years remaining on their current deals.
Warburton insists the players are simply engaged in a standard process of negotiation and believes they are being unfairly depicted in some quarters as lacking commitment towards Rangers.
“I’ve every confidence (they will sign new contracts),” said Warburton, pictured. “They love being here. It was a big move to come here. They committed, their families are in schools and their partners are settled here. They are committed to Glasgow Rangers.
“They love their time here. I’m disappointed for them that they are getting negativity because they don’t deserve it.
“They’ve shown how much it means to play for Glasgow Rangers – and that won’t change.
“I think it’s very harsh on two players who performed as they performed last season. I have no doubt they have thoroughly enjoyed their time at Rangers. Then a story comes out of the blue and the boys are as upset by it as everyone else.
“I think ‘taken out of context’ is the right statement on this. They are two guys who are talking to their advisors and with the club as everyone else does.
“It’s normal practice. But to say these two boys have ‘rejected this’ or some of the comments aimed at them are inappropriate. They are committed to the club. They were magnificent for us last season and I think they will be again this season.
“I hope they will (follow me in signing new contracts). But the same as it was in my case, it goes for them as well – they only had three weeks off after the cup final. They deserved some downtime.
“So we’ve not had a chance to discuss it, we’ve not seen their representatives.
“People are making a big deal of ‘why hasn’t A, B and C happened?’ It’s because of time constraints. I’m sure the two guys are happy here, committed here and we are delighted to have them here too.”
As Rangers prepare for their return to the top flight of Scottish football after a four-year absence, Warburton has no concerns that the speculation over their contractual situations will have a detrimental or unsettling effect on Tavernier and Waghorn.
“No, not at all,” he added. “Their focus is on football. We speak to them every day and we chat and we have an open and honest relationship. There’s no negativity about Tav and Waggy in any shape or form.
“They’ve got two years still to run on their contracts. I’m not talking about private terms and private contracts.
“But they scored 43 goals between them for us last season. Their contribution was clear and they know how it works. They have been given a stage here to flourish. They have responded to our supporters. I hope our supporters know how committed they are, the quality they have shown and their desire to be part of Rangers going forward.
“I’m just disappointed that two players like them are getting negativity at the moment, because they don’t deserve it.”
Rangers managing director Stewart Robertson, meanwhile, has praised both Warburton and his assistant David Weir for the work which has earned the new contracts they formally signed yesterday.
“Our decision to reward Mark and David with significantly improved contracts was primarily driven by our recognition of their role in transforming the football department at all levels throughout the club and their desire to continue with that project in the seasons ahead,” said Robertson.
“We have sold more than 41,000 season tickets and, like everyone at the club, our supporters are looking forward to seeing the team compete in the top flight once again – both domestically and in Europe.
“Mark and David have worked with (head of recruitment) Frank McParland to identify and recruit a number of players for the campaign ahead and we are all relishing Rangers’ return to competitive action under their stewardship.”